NTS GAT General Preparation Guide

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PATTERNS AND
PRACTICE
2 Quantitative Ability
The Quantitative section measures your basic mathematical skills, understanding of elementary
mathematical concepts, and the ability to reason quantitatively and solve problems in a
quantitative setting. There is a balance of questions requiring basic knowledge of arithmetic,
algebra, geometry, and data analysis. These are essential content areas usually studied at the
high school level.

The questions in the quantitative section can also be from

• Discrete Quantitative Question • Quantitative Comparison Question

• Data Interpretation Question etc.

The distribution in this guide is only to facilitate the candidates. This distribution is not a part
of test template, so, a test may contain all the questions of one format or may have a random
number of questions of different formats.

This chapter is divided into 4 major sections. The first discusses the syllabus /contents in each
section of the test respectively and the remaining three sections address the question format,
guide lines to attempt the questions in each format and some example questions.

2.1 General Mathematics Review

2.1.1 Arithmetic

The following are some key points, which are phrased here to refresh your knowledge of basic
arithmetic principles.

Basic arithmetic

• For any number a, exactly one of the following is true:

o a is negative o
a is zero
o a is positive
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a a only if a 0
• The only number that is equal to its opposite is 0 (e.g. =− = )

a 0 0
• If 0 is multiplied to any other number, it will make it zero ( × = ).

• Product or quotient of two numbers of the same sign are always positive and of a different
sign are always negative. E.g. if a positive number is multiplied to a negative number the
result will be negative and if a negative number is divided by another negative number the
result will be positive.

See the following tables for all combinations.

+ ÷ or × + = +

+ ÷ or × − = −

− ÷ or × + = −

− ÷ or × − = +

• The sum of two positive numbers is always positive.

• The sum of two negative numbers is always negative.

• Subtracting a number from another is the same as adding its opposite a−b = a+(−b)
1

a
• The reciprocal of a number a is

1
• The product of a number and its reciprocal is always one a× =1

1
• Dividing by a number is the same as multiplying by its reciprocal a ÷b = a×

b
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• Every integer has a finite set of factors (divisors) and an infinite set of multipliers.

• If a and b are two integers,the following four terms are synonyms o a is a

divisor of b o a is a factor of b o b is a divisible b y a
o b is a multiple of a

They all mean that when a is divided by b there is no remainder.

• Positive integers, other than 1, have at least two positive factors.

• Positive integers, other than 1, which have exactly two factors, are known as prime
numbers.

• Every integer greater than 1 that is not a prime can be written as a product of
primes.
To find the prime factorization of an integer, find any two factors of that number, if both
are primes, you are done; if not, continue factorization until each factor is a prime.
E.g. to find the prime factorization of 48, two factors are 8 and 6. Both of them are not
prime numbers, so continue to factor them.
Factors of 8 are 4 and 2, and of 4 are 2 and 2 (2 × 2 × 2).
Factors of 6 are 3 and 2 (3 × 2).
So the number 48 can be written as 2 × 2 × 2 × 2 × 3.

• The Least Common Multiple (LCM) of two integers a and b is the smallest integer
which is divisible by both a and b, e.g. the LCM of 6 and 9 is 18.

• The Greatest Common Divisor (GCD) of two integers a and b is the largest integer
which divides both a and b, e.g. the GCD of 6 and 9 is 3.

• The product of GCD and LCM of two integers is equal to the products of numbers
itself. E.g. 6 × 9 = 54
3 × 18 = 54 (where 3 is GCD and 18 is LCM of 6 and 9).

• Even numbers are all the multiples of 2 e.g. (… , −4, −2, 0, 2, 4, …)

• Odd numbers are all integers not divisible by 2 ( … , −5, −3, −1, 1, 3, 5, … )

• If two integers are both even or both odd, their sum and difference are even.

• If one integer is even and the other is odd, their sum and difference are odd.

• The product of two integers is even unless both of them are odd.

• When an equation involves more than one operation, it is important to carry them
out in the correct order. The correct order is Parentheses, Exponents, Multiplication
and Division, Addition and Subtraction, or just the first letters PEMDAS to
remember the proper order.
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Exponents and Roots

• Repeated addition of the same number is indicated by multiplication:

17 + 17 + 17 + 17 + 17 = 5 × 17

• Repeated multiplication of the same number is indicated by an exponent:

5
17 × 17 × 17 × 17 × 17 = 17

5
In the expression 17 , 17 is called base and 5 is the exponent.

1 n
• For any number b: b = b and b = b × b × … × b, where b is used n times as
factor.

• For any numbers b and c and positive integers m and n:

o
bb=b mn m+n

b m = m−n
o n b

b
o
(bm)n = bmn
o
bmcm = (bc)m
• If a is negative, a is positive if n is even, and negative
n if n is odd.

9 x 3 x 3
• There are two numbers that satisfy the equation x2 = : = and =− . The

positive one, 3, is called the (principal) square root of 9 and is denoted by symbol
9 . Clearly, each perfect square has a square root:

0 = 0, 9 = 3, 36 = 6, 169 =13, 225 = 25 etc.

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For any positive number a there is a positive number b that satisfies the equation a=b .

• For any positive integer, ( a)2 = a × a = a .

• For any positive numbers a and b:

a = a
ab = a × b and
o b b

a +b ≠ a + b

o
as 5 = 25 = 9 +16 ≠ 9 + 16 = 3 + 4 = 7

( a) =a , a = a is true only if a is
2
• Although it is always true that
2

(−5)2 = 25 = 5 ≠ −5 positive as

• For any number a, a n =a2 .

• For any number a, b and c:

• a(b + c) = ab+ ac a(b −c) = ab − ac

a 0
and if ≠

(b + c) b c (b −c) b c
• = + = − a a a a a a

Inequalities

• For any number a and b, exactly one of the following is true: a>b or a=b or
a<b.

a b a b
• For any number a and b, > means that − is positive.
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a b a b
• For any number a and b, < means that − is negative.

a b a b
• For any number a and b, = means that − is zero.

• The symbol ≥ means greater than or equal to and the symbol ≤ means less than or
x 5
equal to. E.g. the statement ≥ means that x can be 5 or any number greater than
5. The statement 2 < x< 5is an abbreviation of 2 < x and x< 5.

• Adding or subtracting a number to an inequality preserves it.

• If a<b , then a+c<b+cand a−c<b−c .

e.g. 5 < 6 ⇒ 5+10 < 6+10 and 5−10 < 6−10

• Adding inequalities in same direction preserves it:

a c b
If a<b and c<d , then + < +d .

• Multiplying or dividing an inequality by a positive number preserves it. If

a<b and cis a positive number, then a×c<b×c and a < b

cc.
• Multiplying or dividing an inequality by a negative number
reverses it. If

a<b and cis a negative number, then a×c>b×c and a > b

c c.
• If sides of an inequality are both positive and both negative,
taking the reciprocal reverses the inequality.

0 x 1 a a a
• If < < and is positive, then x < .

• 0<x<1and m and nare integers with m > n , then xm < xn

If
<x.
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• If 0< x <1, then x > x.

1 1

If 0 < x<1, then x > xand x >1

•

Properties of Zero

• 0 is the only number that is neither negative nor positive.

• 0 is smaller than every positive number and greater than

every negative number.

• 0 is an even integer.

• 0 is a multiple of every integer.

• For every number a : a+0 = a and a−0 = a .

a a 0 0
• For every number : × = .

n 0
• For every positive integer : 0n = .

a a and a
• For every number (including 0): ÷0 are undefined
symbols.

0 a 0
• For every number a (other than 0): ÷ = 0 = . a

is the only number that is equal to its opposite:

0 0 =−0 .
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• If the product of two or more numbers is 0, at least one of

them is 0.

Properties of One

For any number a : a×1= a and a = a.

1
n
• For any number : 1n =1.

• 1 is the divisor of every integer.

• 1 is the smallest positive integer.

• 1 is an odd integer.

• 1 is not a prime.

Fractions and Decimals

• When a whole is divided into n equal parts, each part is called

one nth of
1
the whole, written . For example, if a pizza is cut (divided) into 8 equal n

slices, each slice is one eighth ( ) of the pizza; a day is divided into 24 equal hours, so an

)
hour is one twenty-fourth ( of a day and an inch is

one twelfth ( ) of a foot. If one works for 8 hours a day, he works eight

twenty-fourth ( ) of a day. If a hockey stick is 40 inches long, it

measures forty twelfths of a foot.

• The numbers such as and , in which one

integer is written
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over the second integer, are called fractions. The center line is called the fraction bar.
The number above the bar is called the numerator, and the number below the bar is
called denominator.

• The denominator of a fraction can never be 0.

• A fraction, such as , in which the denominator is greater

than numerator, is known as a proper fraction. Its value is

less than one.

• A fraction, such as , in which the denominator is less than

numerator, is known as an improper fraction. Its value is

greater than one.

• A fraction, such as, in which the denominator is equal to

the numerator, is also known as an improper fraction. But,

Its value is one.

• Every fraction can be expressed in decimal form (or as a

whole number) by dividing the number by the denominator.
3 3 8 48 100
= 0.3, = 0.75, =1, = 3, =12.5

10 4 8 16 8
• Unlike the examples above, when most fractions are
converted to decimals, the division does not terminate, after
2 or 3 or 4 decimal places; rather it goes on forever with
some set of digits repeating it.
2 3 5 1

= 0.66666..., = 0.272727..., = 0.416666...,=1.133333...

3 11 12 1
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To compare two decimals, follow these rules:

o Whichever number has the greater number to the left of the decimal point is
greater: since 11 > 9, 11.0001 > 9.8965 and since 1 > 0, 1.234 > .8. (Recall that
if a decimal is written without a number on left of decimal point, you may assume
that a 0 is there, so, .8 = 0.8).
o If the numbers to the left of the decimal point are equal, proceed as follows:

• If the numbers do not have the same number of digits to the

right of the decimal point, add zeroes to the end of the
shorter one to make them equal in length.
• Now compare the numbers ignoring the decimal point.
• For example, to compare 1.83 and 1.823, add a 0 to the end
of 1.83 forming 1.830. Now compare them, thinking of them
as whole numbers without decimal point: since 1830 > 1823,
then 1.830 >1.823.

• There are two ways to compare fractions:

o Convert them to decimals by dividing, and use the method already described to

compare these decimals. For example to compare and , convert them to

0.4 0.25
decimals. = and = . Now, as 0.4 > 0.25, > .

o Cross multiply the fractions. For example to compare and ,

cross multiply:

Since 2×4>1×5, then .

• While comparing the fractions, if they have same the
denominators, the
3 2
fraction with the larger numerator is greater. For example > . 5
5

• If the fractions have the same numerator, the fraction

with the
3 3
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smaller denominator is greater. For example > .

5 10
• Two fractions are called equivalent fractions if both of
them have same decimal value.
15
=
• For example, as both of these are equal to
0.5.

2 10
• Another way to check the equivalence of two fractions is to
cross-multiply. If both of the products are same, the fractions
are equivalent. For Example, to compare with , cross-

2 15 6 5
multiply. Since × = × , both of the
fractions are equivalent.

• Every fraction can be reduced to lowest terms by dividing the

numerator and denominator by their greatest common
divisor (GCD). If the GCD is 1,

the fraction is already in lowest terms. For example to reduce , divide both numerator

and denominator by 5 (which is GCD of 10 and 15). This will reduce the fraction to .

• To multiply two fractions, multiply their numerators and

multiply their
3 4 3×4 12
× = =
denominators. For example ×7 35 .

5 7 5
• To multiply a number to a fraction, write that number as a
fraction whose
3 3 7 3×7 21
denominator is 1. For example 5× 7 = 5× 1 = 5 ×1 = 5 .
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• When a problem requires you to find the fraction of a number,

multiply that fraction with the number. For example, to find

two fifth ( ) of 200,

80
2 2 200 400
×200 = × = = 80
multiply: 5 5 1 5/ .

ab a b
• The reciprocal of a fraction is another fraction since
1
× = b a b a

• To divide one fraction by the other fraction, multiply the

reciprocal of
2
22 11 22 7 2
divisor with the dividend. For example, 7 ÷ 7 = 7 × 11 = 1 = 2 .

• To add or subtract the fractions with same denominator, add

or subtract numerators and keep the denominator. For
41 5 4 1 3
+ = example and
− = .

99 9 9 9 9

Percents

• The word percent means hundredth. We use the symbol %

to express the word percent. For example “15 percent”
means “15 hundredths” and can be written with a % symbol,

as a fraction, or as a decimal. 20% = = 0.20.

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• To convert a decimal to a percent, move the decimal point

two places to the right, adding 0s is necessary, and add the
percent symbol (%).
For example, 0.375 = 37.5% 0.3 = 30% 1.25 = 125% 10=1000%

• To convert a fraction to a percent, first convert that fraction

to decimal, than use the method stated above to convert it
to a percent.

• To convert a percent to a decimal, move the decimal point

two places to the left and remove the % symbol. Add 0s if
necessary.
For example, 25% = 0.25 1% =0.01 100% = 1

• You should be familiar with the following basic conversions:

1 5 1 2
= = 0.50 = 50% = = 0.20 = 20 %

2 10 5 10
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= 0.25 = 25% = 0.75 = 75 %

a % a
• For any positive integer : a of 100 is .

a b a% of b b% of a
• For any positive numbers and : =

actual change

• The percent change in the quantity is original amount ×

100% . For example:
If the price of a lamp goes from Rs.80 to Rs.100, the actual increase is
20 1
× Rs.20, and the percent
increase is 100% = ×100% = 25%.

80 4
a b a b
• If < , the percent increase in going from to is always
b a
greater than percent decrease in going from to .

• To increase a number by k%, multiply it by

1+k% , and to
decrease a number by k%, multiply it by 1−k%. For example,
the value of an investment of Rs. 20,000 after 25% increase
is 20,000×(1+ 25%) = 20,000×(1.25) = 25,000.

• If a number is the result of increasing another number by k%,

1 %
to find the original number divide it by +k , and if a
number is the result of decreasing another number by k%, to
find the original number, divide it by 1−k%.
For example, The government announced an 20% increase in salaries. If after the
increment, The salary of a particular employee is Rs. 18, 000, what was the original
salary?
current salary 18,000 18,000
= = =15,000

Original salary (in Rs.) =

1+ percent increase 1+ 20% 1.20
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Ratios and Proportions

• A ratio is a fraction that compares two quantities that are

measured in the same units. The first quantity is the
numerator and the second quantity is denominator. For
example, if there are 16 boys and 4 girls, we say that the
ratio of the number of boys to the number of girls on the team

is 16 to 4, or . This is often written as 16:4. Since a ratio

is just a fraction, it can

be reduced or converted to a decimal or a percent. The Following are different ways to
express the same ratio:
0.25 %
16to 4, 16:4 , , , 25

b
• If a set of objects is divided into two groups in the ration a:
, then the a
first group contains a +b of the total objects and similarly the second group

b
contains a +b of the total number of objects. This rule applies to extended

c
ratios, as well. If a set is divided into three groups in the ratio a:b: , then a
the first group contains a +b+c of the total objects, and so on.

• A proportion is an equation that states that two ratios are

equivalent. Since
4 10
ratios are just fractions, any equation such as = in which each side is

6 15
a single fraction is proportion. This proportion states that 4 relates to 6 in same ratio as 10
relates to 15.
a c
ad bc
• For each proportion of the form = , = . This
property can be used b d
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to solve proportions for unknowns (variables). For example: “If 3 oranges cost Rs.5, how
many oranges can you buy for Rs.100”. To solve this problem we have to set up a
x
proportion. If the number of oranges for Rs.100 is , then:

3 x 3×100
= ⇒ 3×100 = x×5⇒ x = ⇒ x = 60

5 100 5

Averages

• The average of a set of n numbers is the sum of those

numbers divided by n.

n
average = sum of n numbers or simply A = Sum
n
the technical name for these kind of averages is
Arithmetic Mean.

• If you know the average of n numbers, multiply that average

with n to get the sum of numbers.

• If all the numbers in a set are the same, then that number is
the average.

• Assume that the average of a set of numbers is A. If a new

number x is added to that set, the new average will be;

o Greater if x is greater than the existing average o

Smaller if x is smaller than the existing average o
Unchanged if x is equal to the existing average

• Arithmetic sequence is an ordered set of numbers, such that,

the difference between two consecutive numbers is the same.

• If there is an arithmetic sequence of n terms, then the

average calculation can be made simple by using these rules.
o The average of the terms in that sequence will be the middle term, if n is odd.
o If n is even, the average will be the average of two middle terms.

2.1.2 Algebra
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Polynomials

• A monomial is any number or variable or product of numbers

and variables.

For example 3, −4, x, y, 3x, −2xyz, 5x3,1.5xy2, a3b 2 are all monomials.

• The number that appears in front of a variable in a monomial

is called the
3
x
coefficient. The coefficient of 5 is 5. If there is no number, the coefficient is either 1 or –1,
x x x
because means 1 and − means −1x .

• A polynomial is a monomial or the sum of two or more

monomials. Each monomial that makes up the polynomial is
called a term of that polynomial.

• If a polynomial has only one term it is a simple monomial, if

it has two terms, it is known as binomial and if it has three
terms, it is called trinomial.

• Two terms are called like terms if they differ only in their
coefficients. 5x3 and −2x3 are like terms, whereas, 5x 3 and
5x2 are not.

• If like terms are involved in a polynomial, they can be

combined, by adding their coefficients, to make that
polynomial simpler. The polynomial

3x2 + 4x+5x−2x2 −7 is equivalent to the polynomial x2 +9x−7.

• All laws of arithmetic are also applicable to polynomials. Most
important of them is PEMDAS.

• Polynomials can be added, subtracted, multiplied or divided.

• To add two polynomials, put a plus sign between them, erase

the parentheses, and combine like terms.

Example:

What is the sum of 5x2 +10x−7 and 3x2 −4x+2?

Solution:
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(5x2 +10x−7)+(3x2 −4x+ 2)

= 5x2 +10x−7+3x2 −4x+ 2
= 8x2 +6x−5

• To subtract two polynomials, reverse the signs of subtrahend,

and add two polynomials as done before.

Example:

x x
Subtract 3x2 −4 +2 from 5x2 +10 −7

Solution:
(5x2 +10x−7)−(3x2 −4x+ 2)
= (5x2 +10x−7)+(−3x2 + 4x− 2)
= 5x2 +10x−7−3x2 + 4x− 2
= 2x2 +14x−9

• To multiply monomials, first multiply their coefficients, and

then multiply their variables by adding the exponents.

Example: What is the product of 3x2yz from −2x2y

2
?

Solution:
(3x2yz)(−2x2y2 )
= (3×−2)(x2×x2)(y× y2 )(z)
=−6x4y3 z

• To multiply a monomial by a polynomial, just multiply each

term of the polynomial by the monomial.

x 3x
Example: What is the product of 3 from 2 −6xy2 +
2?
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Solution:
(3x)(3x2 −6xy2 + 2)
= (3x×3x2)−(3x×6xy2)+(3x× 2)
= 9x3 −18x2y2 + 6x

• To multiply two binomials, multiply each term of first binomial

by each term of second binomial, then add the results.

Example:
3x+ y 3x2 −6xy2
What is the product of from ?

Solution:
(3x+ y)(3x2 −6xy2 )
= (3x×3x2)+(3x×(−6xy2))+(y×3x2)+(y×(−6xy2 ))
= (9x2)+(−18x2y2)+(3x2y)+(−6xy3 )
= 9x2 −18x2y2 +3x2y−6xy 3

• The three most important binomial products are:

(x− y)(x+ y) = x + xy− xy+ y2 = x2 + y 2
2

o
(x+ y)(x+ y) = x2 + xy+ xy + y2 = x2 + 2xy + y 2
o
(x− y)(x− y) = x2 − xy− xy+ y2 = x2 −2xy+ y 2
o
Memorizing these can save a lot of calculation time during the test.

• To divide a polynomial by a monomial, divide each term of

the polynomial by the monomial.

Example:
32x2y +12xy3z 8xy
What is the quotient if is divided by ?

Solution:

32x2y+12xy3z = 32x2y +12xy3 z = 4x+ 3 y2 z (by reducing the terms)

xy 8xy 8xy 2
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Solving Equations and Inequalities

• The basic principle in solving equations and inequalities is that

you can manipulate them in any way as long as you do the
same thing to both sides. For example you may add a
number to both sides, or you may divide or multiply both
sides with same number etc.

• By using the following six-step method, you can solve most

of the equations and inequalities. The method is explained
with the help of an example.

Example:
x x 2) x 1) x
if +3( − = 2( + +1, what is the value of ?

Solution:

Step What to do… Example

1 Get rid of fractions and decimals Multiply each side by 2 x+6(x−2) = to get:
by multiplying both sides by the
LCD. 4(x+1)+ 2
2 Get rid of all parentheses by x+6x−12=4x+4+2
solving them.
3 Combine like terms on each 7x−12 = 4x+6
side.
4 By adding and subtracting get all x to get:
Subtract 4 from each side
the variables on one side
(mostly left). 3x−12=6
5 By adding or subtracting get all Add 12 to each side 3x to get:
plain numbers on the other side.
=18
6 Divide both sides by the Divide both sides by 3 to get:
coefficient of the variable. (If
x=6
you are dealing with an
inequality and you divide with a
negative number, remember to
reverse the inequality.)

• When you have to solve one variable and the

equation/inequality involve more than one variable, treat all
other variables as plain numbers and apply the six-step
method. Example:

a b c b a c
if =3 − , what is the value of in terms of and ?

Solution:
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Step What to do… Example

1 There are no fractions and decimals.

2 There are no parentheses.

3 There are no like terms.
4 By adding and subtracting get all Remember there is only one
the variables on one side. b
variable , which is on one side
only.
5 By adding or subtracting get all plain Remember we are
numbers on the other side. a c
considering and as plain

c
number. Add to each

side to get: a+c

= 3b
6 Divide both sides by the coefficient of Divide both sides by 3 to get:
the variable. a+c
=b
3
• It is not necessary to follow these steps in the order specified.
Some times it makes the problem much easier, if you change
the order of these steps.

x 4 11 x
Example: If − = , what is the value of
-8?

Solution:

x 15
Going immediately to step 5, add 4 to each side to get: = . Now subtract 8 from both
sides to get: x−8=7 .

• Doing the same thing on each side of an equation does not

mean doing the same thing to each term of the equation. This
is very important if you are doing divisions, or dealing with
exponents and roots.

a 0 a b c
Example: If > and a2 +b2 = c2, what is the value of in terms of and .

a2 b2 c2 a2 c2 b 2
Solution: + = ⇒ = − . Now you can’t take a square root of each term
a c b
to get = − . You must take the square root of each side: a2 = c2 −b2
⇒ a = c2 −b 2
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• Another type of equation is that in which the variable appears

in exponent. These equations are basically solved by
inception. Example:

If 2x+3 = 32, what is the value of 3x+2?

Solution:
2x+3 = 32 ⇒ 2x+3 = 25 ⇒ x+3 = 5 ⇒ x = 2 .

Now as x =2, you can get x = 2 ⇒ x+ 2 = 4 ⇒ 3x+2 = 34 = 81

• A system of equations is a set of two or more equations

having two or more variables. To solve such equations, you
must find the value of each variable that will make each
equation true.

• To solve a system of equations, add or subtract them to get

a third equation. If there are more than two equations you
can just add them.

Example:

If x+ y =10 and x− y =10 what is the value of y ?

Solution:
x+ y =10 x− y = 2
Add two equations: 2x =12 ⇒ x = 6

Now replacing x with 6 in the first equation: 6+ y =10 ⇒ y = 4

• If you know the value of one variable in a system of two

equations, you can use this value to get the value of the other
variable. As it is done in the previous question.

Word problems
• To solve word problems, first translate the problem from
English to Algebra. While translating, use variables to
represent unknowns. Once translated, it is easy to solve them
using the techniques you have learned in previous sections.
• Following English to Algebra dictionary will be helpful in
translating word problems to algebraic expressions.

Mathematical meaning
English words Symbol
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Is, was, will be, had, has, will have, is Equals =

equal to, is the same as
Plus, more than, sum, increased by, Addition +
added to, exceeds, received, got, older
than, farther than, greater than

Minus, fewer, less than, difference, Subtraction −

decreased by, subtracted from, younger
than, gave, lost

Times, of, product, multiplied by Multiplication ×

Divided by, quotient, per, for Division ÷ or
a
b

More than, greater than Inequality

At least Inequality
Fewer than, less than Inequality
At most Inequality
What, how many, etc. Unknown quantity x
(Some variable)

Examples:

o
The sum of 5 and some number is 13. 5+ x =13
o Javed was two years younger than Saleem. J = S −2
o Bilal has at most Rs.10,000. B ≤10000
o The product of 2 and a number exceeds that
number by 5 (is 5 more than that number). 2N = N +5

• In word problems, you must be sure about what you are

answering. Do not answer the wrong question.

• In problems involving ages, remember that “years ago”

means you need to subtract, and “years from now” means
you need to add.

• Distance problems all depend on three variations of the same

formula:
o distance = speed×time
speed = distance o time

time = distance
speed o
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Example:
How much longer, in seconds, is required to drive 1 mile at 40 miles per hour than at 60
miles per hour?

Solution:
The time to drive at 40 miles per hour can be calculated as

1 1 × 60 3 3 × 6030
time1 = 40 hours = 40 2 minutes = 2 seconds =

90seconds

The time to drive at 60 miles per hour can be calculated as

1

2 60 1 60 60
time = hours = 60 × minutes = × seconds = seconds

difference = time1−time2 = 90−60 = 30 seconds.

2.1.3 Geometry

Lines and Angles

• An angle is formed at the intersection of two line segments,

rays or lines. The point of intersection is called the vertex.
Angles are measured in degrees.

• Angles are classified according

to their degree measures.
• An acute angle measures less
than

90°
• A right angle measures
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90° 180°
• An obtuse angle measures more than but less than

180°
• A straight angle measures

• If two or more angles combine together to form a straight

180°
angle, the sum of their measures is .

a°+b°+c°+d°=180°

• The sum of all the measures of all the angles around a point
360°
is

a°+b°+c°+ d°+e°=360°

• When two lines intersect, four angles are formed, two angles
in each pair of opposite angles are called vertical angles.
Vertical angles, formed by the intersection of two lines, have
equal measures.

a = c and b = d

• If one of the angles formed by the intersection of two lines is

a right angle, then all four angles are right angles. Such lines
are called perpendicular lines

a = b = c =90

• In the figure below a line l divides the angle in two equal

parts. This line is said to bisect the angle. The other line k
bisects another line into two equal parts. This line is said to
bisect a line.
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• Two lines are said to be parallel, if they never intersect each

other. However, if a third line, called a transversal,
intersects a pair of parallel lines, eight angles are formed.
And the relationship among theses angles is shown in the
following diagram. • - All four acute angles are equal
a=c=e=g
• - All four obtuse angles are equal b=d=f=h
• - The sum of any pair of acute and

180°
• obtuse angle is , e.g.

a+d =180°,d +e =180°,b+ g =180° etc.

Triangles
• In any triangle, the sum of the measures of the three angles
180°
is .

x+ y + z =180

• In any triangle:
o The longest side of triangle is opposite the largest angle. o The
shortest side is opposite the smallest angle.
o Sides with the same length are opposite the angles with the same
measure.

• Triangles are classified into three different kinds with respect

to the lengths of sides.
o Scalene: in which all three sides are of different lengths.
o Isosceles: in which two of the sides of triangle are equal in length, the third is
different.
o Equilateral: in which all three sides are equal in length.

• Triangles are also classified with respect to the angles.

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o Acute triangle: in which all three angles are acute. o Obtuse triangle: in
which one angle is obtuse and two are acute.
o Right triangle: This has one right and two acute angles.

• In a right triangle, the opposite to the right angle is known as

hypotenuse and is the longest side. The other two sides are
called legs.

• In any right triangle, the sum of the measures of the two

acute angles is 90°.

• By Pythagorean Theorem, the sum of squares of the lengths

of legs of a right triangle is always equal to the square of
length of hypotenuse.

a2 +b2 = c2
• In any triangle, the sum of any two sides is always
greater than the third one. And the difference of any two
sides is always less than the third one.

a +b > c and a −b < c

• The perimeter of a triangle is calculated by adding the

lengths of all the sides of that triangle.

perimeter = a+b+c
1
area = bh
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2
• The area of a triangle is calculated by the formula:
b h
where is the base of the triangle and is the height of the
triangle.
o Any side of triangle can be taken as the base.
o Height is the altitude (perpendicular) drawn to the base from its opposite vertex.
o In a right triangle any leg could be taken as the base, the other will be the
altitude.

Quadrilateral and other Polygons

• A polygon is a closed geometric figure, made up of line

segments. The line segments are called sides and the end
points of lines are called vertices (plural of vertex). Lines,
inside the polygon, drawn from one vertex to the other, are
called diagonals.

n n
• The sum of the measures of the angles in a polygon with
sides is always (n−2)×180° .

• In any quadrilateral, the sum of the measures of the four

360°
angles is .

• A regular polygon is a polygon in which all of the sides are

of the same length. In any regular polygon, the measure of
each interior angle is
(n−2)×180° 360°
and the measure of each exterior angle is .
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n n
• A parallelogram is a special quadrilateral, in which both
pairs of opposite sides are parallel. The Following are some
properties of parallelogram.

B CD D BC
o Lengths of opposite sides are equal. A = and A = o Measures of
a c b d 180°
opposite angles are equal. = and = o Consecutive angles add up to .

a b 180° b c 180°
+ = , + = etc.

AE EC E
o The two diagonals bisect each other. = and B = ED o A diagonal
divides the parallelogram into two triangles that are congruent.

• A rectangle is a parallelogram in which all four angles are

right angles. It has all the properties of a parallelogram. In
addition it has the following properties:

90°
o The measure of each angle in a rectangle is . o
The diagonals of a rectangle are equal in length.

• A square is a rectangle that has the following additional

properties:
o A square has all its sides equal in length.
o In a square, diagonals are perpendicular to each other.
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• To calculate the area, the following formulas are required:

Area bh b h
o For a parallelogram, = , where is the base and is the height. o For a
rea lw l w
rectangle, A = , where is the length and is the width.

rea s
o For a square, A = s2 , where is the side of the square.

• Perimeter for any polygon is the sum of lengths, of all its

sides.
Circles

• A circle consists of all the points that are the same distance
from one fixed point called the center. That distance is called
the radius of a circle. The word radius is also used to
represent any of the line segments joining the center and a
point on the circle. The plural of radius is radii.

CED
• Any triangle, such as in the figure, formed by
connecting the end points of two radii, is an isosceles.

• A line segment, such as ED in the diagram above, both of

whose end points are on a circle is called a chord.

• A chord that passes through the center of the circle is called

the diameter of the circle. The length of the diameter is
always double the radius of the circle. The diameter is the
longest cord that can be drawn in a circle.

• The total length around a circle is known as the

circumference of the circle.

• The ratio of the circumference to the diameter is always the

same for any circle. This ratio is denoted by the symbol π
(pronounced as pi).

2
• π= C ⇒ C =πd ⇒ C = πr where C is the circumference,
d is the diameter d
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and r is the radius of the circle.

π 3.14
• Value of is approximately

• An arc consists of two points in a circle and all the points

between them. E.g. PQis an arc in the diagram.

• An angle whose vertex is at the center of the circle is called

the central

angle. ∠PCQ in the diagram above is a central angle.

360°
• The degree measure of a complete circle is .

• The degree measure of an arc is the measure of the central

angle that intercepts it. E.g. the degree measure of PQ is
equal to the measure of ∠PCQ in the diagram above.
x
x
• If is the degree measure of an arc, its length can be
C
calculated as , 360

where C is the circumference.

• πr2 .
The area of a circle can be calculated as
• The area of a sector formed by the arc and
two radii can be x
calculated as A, where A is the area of a circle.

360

2.2 Discrete Quantitative Questions

These are standard multiple-choice questions. Most of such questions require you to do some
computations and you have to choose exactly one of the available choices based upon those
computations. This section will teach you the basic tactics to attempt such questions.
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2.2.1 Question format

Each question will consist of a question statement and the choices labeled from A to E. The
number of choices may vary from 2 to 5, but exactly one choice will be correct for each question.
2.2.2 How to attempt?

Following are some tactics, which will lead you to the correct answer.

• Whenever you know how to answer a question directly, just

do it. The tactics should be used only when you do not know
the exact solution, and you just want to eliminate the choices.

• Remember that no problem requires lengthy or difficult

computations. If you find yourself doing a lot of complex
arithmetic, think again. You may be going in the wrong
direction.

• Whenever there is a question with some unknowns

(variables), replace them with the appropriate numeric values
for ease of calculation.

• When you need to replace variables with values, choose easy-

to-use numbers, e.g. the number 100 is appropriate in most
percent-related problems and the LCD (least common
denominator) is best suited in questions that involve
fractions.

• Apply “back-solving” whenever you know what to do to

answer the question but you want to avoid doing algebra. To
understand this tactic read the following example:

On Monday, a storeowner received a shipment of books. On Tuesday, she sold half of them.
On Wednesday after two more were sold, she had exactly 2/5 of the books left. How many
were in the shipment?

(A) 10 (B) 20 (C) 30 (D) 40 (E) 50

now by this tactic:

Assume that (A) is the correct answer, if so; she must have 3 books on Wednesday. But 2/5
of 10 are 4, so, (A) is incorrect;

Assume that (B) is the correct answer, if so; she must have 8 books on Wednesday. 2/5 of
20 are 8, so, (B) is the correct choice, and as there may be only one correct choice, there
is no need to check for remaining choices.

This tactic is very helpful when a normal algebraic solution for the problem involves complex
or lengthy calculations.
• If you are not sure how to answer the question, do not leave
it unanswered. Try to eliminate absurd choices and guess
from the remaining ones. Most of the times four of the choices
are absurd and your answer is no longer a guess.
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Many things may help you to realize that a particular choice is absurd. Some of them are
listed below.

o The answer must be positive but some of the choices are negative so eliminate
all the negative ones.
o The answer must be even but some of the choices are odd so eliminate all the
odd choices.
o The answer must be less then 100, but some of the choices are greater than 100
(or any other value) so eliminate all choices that are out of range.
o The answer must be a whole number, but some of the choices are fractions so
eliminate all fractions.
o These are some examples. There may be numerous situations where you can
apply this tactic and find the correct answer even if you do not know the right
way to solve the problem.

Example questions with solutions

The following are some examples, which will help you to master these types of questions.

Example
If 25% of 220 equals 5.5% of X, what is X?
(A) 10 (B) 55 (C) 100 (D) 110 (E) 1000

Solution:
Since 5.5% of X equals 25% of 220, X is much greater than 220. So, choices A, B, C, and D
are immediately eliminated because these are not larger than 220. And the correct answer is
choice E.

(Note: An important point here is that, even if you know how to solve a problem, if
you immediately see that four of the five choices are absurd, just pick the remaining
choice and move on.)

Example
Science students choose exactly one of three fields (i.e. medical sciences, engineering sciences
and computer sciences). If, in a college, three-fifths of the students choose medical sciences,
one-forth of the remaining students take computer sciences, what percent of the students take
engineering sciences?

(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

Solution:
The least common denominator of 3/5 and 1/4 is 20, so assume that there are 20 students in
that college. Then the number of students choosing medical sciences is 12 (3/4 of 20). Of the
remaining 8 students, 2 (1/4 of 8) choose computer sciences. The remaining 6 choose
engineering sciences. As 6 is 30% of 20, the answer is E.

Example
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If a school cafeteria needs C cans of soup each week for each student and there are S students,
for how many weeks will X cans of soup last?

(A) CX/S (B) XS/C (C) S/CX (D) X/CS (E) CSX

Solution:
Replace C, S and X with three easy to use numbers. Let C=2, S=5 and X=20. Now each student
will need 2 cans per week and there are 5 students, so 10 cans are needed per week and 20
cans will last for 2 weeks. Now put these values in choices to find the correct one.
The choices A, B, C, D and E become 8, 50, 1/8, 2 and 200 respectively. So the choice D
represents the correct answer.

2.3 Quantitative Comparison Questions

Some of the questions in the Quantitative section of the test may be quantitative comparison
questions. The Following text will explain you the format and techniques u need to attempt the
questions of this format.

2.3.1 Question format

Such questions consist of two quantities, one in column A and the other in column B. You have
to compare the two quantities. The information concerning one or both quantities is presented
before them. Only the following four choices will be given:

A. The quantity in column A is greater B. The

quantity in column B is greater
C. The two quantities in both columns are equal
D. The relationship cannot be determined from the information given

And as it is clear from the choices, only one will be correct at one time. Your job is to
choose one of them after careful comparison. The following text explains some simple
tactics to attempt such questions.

2.3.2 How to attempt

Whenever you encounter a quantitative comparison question, the following guidelines will help
you to find the correct answer quickly.

• If the question involves some variables, replace them with appropriate numbers. Here are
some guidelines in choosing an appropriate number: o The very best numbers to use are –
1, 0 and 1. o Often fractions between 0 and 1 are useful (e.g. 1/2, 3/4 etc.). o Occasionally,
“large” numbers such as 10 or 100 can be used.
o If there is more than one variable, it is permissible to replace each with the same
number. o Do not impose any un-specified conditions on numbers. Choose them
randomly.

• Eliminate the choices and choose from the remaining ones. For example If you found the
quantities ever equal, the correct choice could never be A or B, so, eliminate A and B.
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• A quantitative comparison question can be treated as an equation or inequality. Either:

Column A < Column B, or
Column A = Column B, or
Column A > Column B
So, you can perform similar operation on both columns to simplify the problem just as in
equations (or inequalities).

Example:
m > 0 and m ≠ 1

m2 m3

• In this example divide both the quantities by m2. This will change column A to 1 and column
B to m. Now the comparison is very simple, as we know that m is greater than 0 and cannot
be 1. So the relationship is not determinable using the current information. m can be both
greater than 1 or between 0 and less than 1.

2.3.3 Example questions with Answers and

Explanations

Example 1:
A student earned a 75 on each of her first three math tests
and an 80 on her fourth and fifth tests.

A B

Average after 4 tests Average after 5 tests

A. The quantity in column A is greater B. The

quantity in column B is greater
C. The two quantities in both columns are equal
D. The relationship cannot be determined from the information given

Remember you want to know which average is higher, not what the averages are. After 4 tests,
the average is clearly less than 80, so an 80 on the fifth test had to raise the average. So the
answer is choice (B).

Example 2:
A B

The time it takes to drive 40 The time it takes to drive 35

miles at 35 miles at 40 mph
mph
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A. The quantity in column A is greater B. The
quantity in column B is greater
C. The two quantities in both columns are equal
D. The relationship cannot be determined from the information given
Once again there is no need for calculation, as the speed in column B is higher than that in
column A. It is obvious that it will take less time to travel shorter distance at a greater speed.
So the value in column A is larger. The answer is option (A).

Example 3:
A B

5
5

A. The quantity in column A is greater B. The

quantity in column B is greater
C. The two quantities in both columns are equal
D. The relationship cannot be determined from the information given

20 2 20 5 2 25

5 5
2 =4 =5 = =5
Square each column: and . So both columns are equal and the answer is choice (C).

Example 4:
A B

13y 15y

To solve this question, subtract 13y from both columns to get 13y −13y = 0 for column A and

15y −13y = 2y for column B. As there are no restrictions, 2y can be greater than, less than
or equal to 0. So the correct choice is (D).

2.4 Data Interpretation Questions

These questions are based on the information that is presented in the form of a graph, chart or
table. Most of the data is presented graphically. The most common types of graphs are line
graphs, bar graphs and circle graphs. The objective of such questions is to test your ability to
understand and analyze statistical data.

2.4.1 Question Format

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Data interpretation questions always appear in sets, you are presented with some data in any
format (chart, graph or table), and you will then be asked with some questions about that data.

The following example explains the format of such questions.

Example:

Question 1:
What is the average sale, in million Rs., for the period 1994-2000?
(A) 5.5 (B) 6.0 (C) 7.0 (D) 8.0
(E) 8.5

Question 2:

For which year, the percentage increase in sales from the previous year is the greatest.
(A) 1995 (B) 1996 (C) 1999 (D) 2000
(E) 2001

2.4.2 How to attempt

• Do not try to answer such questions immediately, first of all read the presented data
carefully. You must be very clear about the data and its meanings even before reading
the first question.

• Do not confuse numbers with percents. This confusion is most likely to occur when data
is presented in pie graphs. For example in the following graph
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12
10
8
6
4
2
0
1994 1995 1996 1997 1998 1999 2000 2001
Years

Now it would be a great mistake here to think that sales of “TVs & VCRs” is
15% more than the sales of Computers in 2001 by XYZ Corporation. To
15 ×100 = 60
%

25
know this you have to calculate it as .
• Try to avoid un-necessary calculations. Most of the questions could easily be solved by
observation and estimation. Use estimation to eliminate the choices, if you are not able
to find the correct answer without calculation. For example to solve “Question 1”
presented in the example at the start of this section, if you are not sure of the correct
answer, you can then try to cut down the number of possible choices by observation.
You are being asked to tell the percentage increase. Where as, in year 2000, the sale is
decreasing instead of increasing, so, you can immediately eliminate choice (D) in that
question.

• Your answers must be based upon the information presented in the given charts and
graphs. If your knowledge contradicts any of the data presented, ignore what you know
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and stick to the presented data. The presented data should be the only base for your
calculations and estimations.

• Always use the proper units, there may be some questions that ask you to compare
different data items possibly from different data sets. Be careful about the units used
to represent the data.

• Because graphs and charts present data in a form that enables you to readily see the
relationships among values and to make quick comparisons, you should always try to
visualize you answer in the same format as the original data was presented.
• Be sure that your answer is reasonable. For example, the profit could never increase
the actual sales, or the expenses could never be negative etc. While answering the
question, first of all eliminate such unreasonable choices, and then choose from the
remaining ones.

2.5 Practice exercise

1 What is the average of positive integers from 1 to 100 inclusive?

(A) 49
(B) 49.5
(C) 50
(D) 50.5
(E) 51

x z 9 x y
2 If x+ y = 6, y + z = 7 , and + = , what is the average of , and z ?

(D) 11 (E) 22

(A) (B) (C)

3 In the diagram below, lines l and m are not parallel.

If A represents the average measure of all the eight angles, what is the value of A?
(A) A =45
(B) 45 < A< 90
(C) A =90
(D) 90 < A<180
(E) A =180
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4 Aslam has 4 times as many books as Salman and 5 times as many as Javed. If Javed has
more than 40 books, what is the least number of books that Aslam could have?

(A) 200 (B) 205 (C) 210 (D) 220 (E) 24

5 Aslam is now 3 times as old as Javed, but 5 years ago, he was 5 times as Javed was. How
old is Aslam now?

(A) 10 (B) 12 (C) 24 (D) 30 (E) 36

% y
6 Ifx of is 10, what is y?
10
(A) x

100
(B) x

1000
(C) x

x
(D)

100
x
(E)

10

Answer Key

1D
2 A
3 A
4 D
5 D
6 C
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3 Analytical Ability
3.1.1 Question format

Each analytical reasoning question is a logical puzzle, based on a given set of conditions. Like
mathematical questions, these questions have exactly one correct answer, which is what you
need to select.

Analytical reasoning questions are presented in groups of four or five questions. Each group is
based on a short passage followed by a set of conditions. Occasionally, there are graphs and
tables instead of a passage. To understand the general format of the question, consider the
following example.

Question 1-4:
As part of their sports physical, seven college athletes F, G, H, I, J, K and L are being weighed.
In announcing the results of the physical exams, the coach has given the following information.
i. None of the athletes is exactly the same weight as another athlete.
ii. K is heavier than L, but lighter than H.
iii. I is heavier than J
iv. Both F and G are heavier than H.

1 Each of the following could be true EXCEPT A. F is the heaviest.

B. G is the heaviest.
C. I is the heaviest.
D. More than three athletes are heavier than K.
E. More than three athletes are lighter than K.

2 Which of the following, if true, would be sufficient to determine which athlete is the lightest?
A. I is the heaviest
B. I is lighter than K
C. K is heavier than J
D. J is heavier than K
E. Exactly five students are lighter than F.

3 If J is heavier than F, how many different rankings by weight, of the athletes are possible?
A. 1 B. 2 C. 3 D. 4 E. 5

4 If H is heavier than I, which of the following CANNOT be true?

A. I’s weight is equal to the average of F’s weight and G’s weight.
B. I’s weight is equal to the average of K’s weight and L’s weight C. J’s weight is equal to the
average of K’s weight and L’s weight
D. J is the second lightest.

Answers:

1. E 2. D 3. C 4. A
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3.1.2 How to attempt

• Simplify the information by using abbreviations and symbols. The first step is to strip
away all of the excess verbiage from the given passage and then to abbreviate the
remaining key words with single letters. For example, in the question statement “five
musicians a bassist, a drummer, a guitarist, a pianist, and a trumpeter are performing
in a talent show”, you should immediately abbreviate them B, D, G, P and T.
You can use abbreviated letters to represent a whole sentence also. You should use
symbols to represent conditions. You may develop your own symbolic conventions for
this. The objective is to convert the problem into notations, so that, it is easily
understandable. The following is a basic set of symbols, which are most commonly used.
‘A’ represents the statement “Akbar is going”.

‘B’ represents the statement “Babur is going”.

Symbo
Meaning Examples
l
~ Not ~A Akbar is not going. Or you can say, “it is not
the case that Akbar is going”.

∧ And A ∧B Akbar and Babur are going.

Akbar is going and Babur is not going.
A ∧~B

∨ Or A ∨B Akbar or Babur is going.

Akbar is going or Babur is not going.
A ∨~B

→ If, then → If Akbar is going then Babur is going.

A B If Akbar and Babur are going, then Saleem is
going.
∧B)
(A
→S
↔ If and only if ↔A Babur is going, if and only if Akbar is going.

• Before learning the tactics to attempt an analytical reasoning question, you must be
familiar with some basic logic facts, which are explained in the following text. Consider
A and B are two statements.
o A is true means ~A is false. o ~A is true
means A is false. o (A ∧ B) is true means
both A and B are true. o (A ∧ B) is true
means either A or B or both are false. o (A
∨B) is true means either A or B or both are
true. o (A ∨B) is false means both A and B
are false. o ~(A ∧B) is equivalent to (~A
∨~B). o ~(A ∨B) is equivalent to (~A
∧~B).
o If (A → B) is true then If A is true B is also
true.
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If A is false B may be true or false. o If (A → B) is

false then A is true and B is false.
o (A →B) is equivalent to (~B → ~A) o (A ↔
B) is true means:
If A is true B is true.
If A is false B is false. o (A ↔
B) is false means:
If A is true B is false. If A is false B is true. o (A
↔B) is equivalent to [(A → B) ∧ (B → A)].

• You must be familiar with the most common types of analytical reasoning questions. The
following four types occur more frequently than the others, and when you see them, you
should immediately know what you need to do to answer them.
o Which of the following could be true? If only one of the answer choices could
be true, then each of the other four choices must be false; that is, each one must
violate at least one of the given conditions.

o Which of the following must be true? Since only one of the answer choices
must be true, then for each of the choices, either it is false or it is possibly (but
not definitely) true. You have to choose only that choice which is definitely true.

o Which of the following cannot be true? Since only one of the answer choices
cannot be true, then each of the other choices could be true. The correct answer
is the only choice, which violates at least one of the given conditions or is
otherwise inconsistent with what you know must be true.
o How many possibilities are there? This question asks, “How many different
ways are there to satisfy all of the given conditions?” Here, you must
systematically count or list all of the possibilities that do not violate any of the
conditions.

• Identify the key words that serve to limit the situation. Certain words are critical to your
understanding of the situation. Be sure to incorporate your symbols. Some frequently
used key words are listed below:

After All Always At least At most

Before But Can be Cannot be Consecutive
No fewer
Different Directly Each No more than
than
Only Possible Entire Every Exactly
Except Fewer First If If and only if
Immediately Impossible Last Least Most
Must be Same Some The Least The Most
Unless Smallest Greatest None

Note that certain key words have only one function, to rule out a
potential ambiguity.
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• Eliminating the choices is always a good strategy. While eliminating the choices, first of
all, eliminate those which are ruled out by individual conditions: Then work through the
remaining choices.

• Study conditions, not merely for what they state but also for what they imply. Certain
analytical reasoning questions resemble the inference questions you find in the reading
comprehension section. To answer them correctly, you must understand not only what
the conditions state explicitly, but also what they imply.

• Often the key to answering analytical reasoning questions is to organize the given
information in a list or table.
• On some analytical reasoning questions, an excellent way to deal with the information is
to draw a simple diagram, picture, or map. This is particularly helpful when you are
dealing with the physical or temporal order of things. It is much easier to tell whether
person A can be seated opposite person B if you have sketched a diagram of the table;
it is easier to know whether person C is older or younger than person D if you have
entered all of the given information on a time line; and it is easier to determine whether
town E is east of town W if you have drawn a simple map.

3.1.3 Example questions with Answers and

Explanations

Questions 1-5:
Six actors ---- Bob, Carol, Dave Ed, Frank, and Grace audition for a part in an off-Broadway play.
The auditions will take place over four consecutive days, starting on a Thursday. Each actor will
have one audition; the days on which the different actors will audition must conform to the
following conditions.

i. At least one audition will take place each day.

ii. No more than two auditions will take place on any day.
iii. No more than three auditions will take place on any two consecutive days.
iv. Bob’s audition must take place on Saturday.
v. Carol’s audition must take place on the same day as another audition. vi. Frank’s auditions
must take place on the day before Grace’s audition.
vii. Dave’s audition must take place on a day after Ed’s audition.

1 If only one audition takes place on Thursday which actor could have that audition?
(A) Bob (B) Carol (C) Dave (D) Frank (E) Grace

2 If Bob’s and Frank’s auditions are on the same day, which of the following must be true
(A) Dave’s audition will take place on Thursday
(B) Dave’s audition will take place on Friday
(C) Grace’s audition will take place on Thursday
(D) Carol’s audition will take place on Sunday
(E) Ed’s audition will take place on Sunday

3 If the director decides to hold two auditions on Thursday and two on Sunday, how many actors would
be eligible to audition on Friday?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
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4 If Ed and Grace have their auditions on the same day which of the following must be true?
(A) Ed’s audition will take place on Thursday.
(B) Frank’s audition will take place on Friday.
(C) Carol’s audition will take place on Saturday.
(D) Grace’s audition will take place on Saturday.
(E) Carol’s audition will take place on Sunday.

5 If Ed’s audition is on Saturday, which of the following actors cannot audition on the same day as any
other actor?
(A) Bob (C) Ed (E) Gr
(B) Carol (D) Frank ace

Questions 6-10:
During the first half of the year, from January through June, the chairperson of the mathematics
department will be on sabbatical. The dean of the college has asked each of the six professors
in the department --- Arkes, Borofsky, Chang, Denture, Hobbes, and Lee--- to serve as acting
chairperson during one of those months. The mathematicians can decide the order in which they
will serve, subject only to the following criteria established by the dean.
i. Chang will serve as chairperson in February.
ii. Arkes will serve as chairperson before Hobbes does.
iii. Borofsky and Dexter will serve as chairpersons in consecutive months.

6 Which of the following professors could serve as chairperson in January?

(A) Borodfsky (B) Chang (C) Dexter (D) Hobbes (E) Lee

7 In how many ways can the schedule be made up if Lee has to serve as chairperson in May?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6

8 If Lee serves in April, all of the following could be true EXCEPT

(A) Arkes serves in January (B) Hobbes serves in march
(C) Borofsky serves in may
(D) Borofsky serves in June
(E) Hobbes serves in June
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9 If Borofsky serves in May, what is the latest month in which Arkes could serve?
(A) January
(B) February
(C) March
(D) April
(E) June

10 Which of the following CANNOT be true?

(A) Arkes and Lee serve in consecutive months.
(B) Lee and Hobbes serve in consecutive months.
(C) Hobbes and Dexter serve in consecutive months.
(D) Arkes and Chang serve in consecutive months.
(E) Borofsky and Chang serve in consecutive months.

Solutions 1-5:
First express each of the conditions symbolically:
B, C, D, E, F, and G: 1 audition each
Days: Thu, Fri, Sat, Sun
Each day: 1 or 2 auditions
2 consecutive days: 2 or 3 auditions
B=Sat C x F<G E<D
1 A violates the condition that Bob’s audition will take place on Saturday (B=Sat). B violates the
condition that Carol’s audition cannot be the only audition on a particular day (C x). Choices C
and E are impossible. Since Dave’s audition must take place on a day after Ed’s audition (E<D)
and Grace’s audition must take place on a day after Frank’s audition (F<G) neither can take
place on Thursday. Only choice D does not violate any of the given conditions, so this is the
correct answer.

2 The condition that Bob’s and Frank’s auditions are on the same day completely determines the
schedule. They must take place on Saturday (B=Sat). To avoid having more than three
auditions on two consecutive days, there can be only one audition on Friday and one on Sunday,
which means there will be two on Thursday. Since Frank must have to precede Grace (F<G),
Grace’s audition will take place on Sunday. Since Ed must precede Dave, Ed’s audition will take
place on Thursday and Dave’s audition on Friday. Finally, Carol’s audition will be the second
audition on Thursday. The final schedule is “C and E on Thursday, D on Friday, B and F on
Saturday and G on Sunday”. Only choice B is consistent with this schedule, so “B” is the correct
choice.

3 Since only one audition can take place on Friday, it cannot be Carol’s (C x); and, of course, it
cannot be Bob’s (B = Sat). Any of the other four actors could audition on Friday as indicated in
the following schedules:
E/F on Thu, D on Fri, B on Sat, C/G on Sun C/F on Thu,
E on Fri, B on Sat, D/G on Sun
C/E on Thu, E on Fri, B on Sat, D/G on Sun E/F on
Thu, G on Fri, B on Sat, C/D on Sun So the correct
choice is D.

4 The only schedule that fulfils the conditions is “F on Thu, E/G on Fri, B on Sat, and C/D on Sun”.
Only choice E is consistent with this schedule.

5 Since Ed and Bob’s auditions are both taking place on Saturday, eliminate choices A and C.
Since Carole must audition on the same day as another actor, eliminate B. Finally, since Dave’s
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audition must take place on Sunday (E < D), Frank’s audition must take place on Thursday and
Grace’s audition on Friday (F < G). Eliminate choice D. The complete schedule is: “C/F on Thu,
G on Fri, B/F on Sat, and D on Sun.” Solutions 6-10:
Let A, B, C, D, H, L represents professor names. C=February, A<H, B<<D
and D<<B

6 Only choice E is there, which does not violate any of the conditions, so is the correct choice.

7 With C serving in February and L in May, the only consecutive months available for B and D are
March and April. Then since A must serve is before H in June. There are two possible schedules,
depending on the order of B and D, so the correct choice is B.

8 If L serves in April, the consecutive months available for B and D are May and June; so choices
C and D could be true. Since A must serve before H, choices A and B must be true, only choice
E cannot be true.

9 Since A must serve before H does, A cannot serve in June. Can A serve in April? No, because
then, D would serve in June (B<<D or D<<B), and again A would not precede H. The latest
that A could serve in March, which could occur in the final order: L, C, A, D, B and H.

10 The only professors that can serve in January are A and L, so, one of them must serve in
January, and neither serves in February. So choice A cannot be true.

3.2 Logical Reasoning

Each logical reasoning question requires you to analyze an argument presented in a short passage.
Often you are asked either to find a conclusion that is a logical consequence of the passage, or to
choose a statement that, if true, strengthen or weakens the argument.

3.2.1 Question format

Logical reasoning questions are based upon a passage called argument. You have to analyze the
argument presented in the passage. The passage is followed by a question. Occasionally, there is
more than one question related be the same passage. No matter what the number is, the questions
always aim at your ability to understand the conclusion reached by the author of the passage, and
to give argument and contra arguments. Logical reasoning questions are a lot like reading
comprehension questions in a verbal section.

For each logical reasoning question, the argument is followed by a multi choice question. The
choices are simple statements. Mostly the question statement begins with the phrase “which of the
following statements”. Here are a few examples:
• Which of the following statements is an assumption on which the conclusion of this argument
is based?

• Which of the following statements identifies a flaw in the reasoning of this argument?

• Which of the following statements can be most reasonably inferred, from the statements in
the given passage?

• Which of the following statements, if true, would most seriously, weaken the argument
offered?
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• Which of the following statements, if true, would strengthen the conclusion in the preceding
argument?

• Which of the following statements would be the most important to know to evaluate the
argument given in the preceding paragraph? Every logical reasoning question does not fit
this mold, but you should try.

3.2.2 How to attempt

• While attempting logical reasoning questions, you should read the question statement
before reading the argument. Then you should analyze the argument presented in the
passage. You must know what aspect of the argument you are to concentrate on, and focus
on it. By this, you will not be unnecessarily wasting your time.
• You must be able to spot the question type by reading the question statement. If you do
this, you will be better able to approach the argument in hand. The following six categories
are those which most commonly occur:

1 Assumption: Questions that test your ability to recognize the premises on which an
argument is based, often take the following forms:
o The conclusion above depends on which of the following assumptions?
o The author of the passage above makes which of the following assumptions?
o In the passage above, the author assumes which of the following statement to
be true?

2 Inference: Questions, which test your ability to go beyond the author’s explicit statements
and see what these statements imply, may be worded like these.
o It can be inferred from the passage above that the author believes that …
o Which of the following is implied by the passage above?
o From the information above, which of the following is the most reasonable
inference?

3 Conclusion: Questions that test your ability to determine what claim can logically be made
on the basis of evidence in the passage above? o If the statements above are true, which of the
following in a conclusion that can be properly drawn?
o The statements in the passage, if true, best supports which of the following
conclusions?

4 Central Point: Questions that test your ability to understand the thrust of an argument.
o The statement sited above conveys which of the following propositions?
o The author of the passage above argues that…
o Which of the following expresses the point the author of the passage above
makes?

5 Support: Questions that test your ability to recognize whether an assertion supports or
undermines an argument. o Which of the following, if true, best supports the author’s
conclusion?
o Which of the following, if true, most weakens the author’s conclusion?
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6 Argument Evaluation: Questions that test your ability to judge an

argument.
o Which of the following identifies a flaw in the speaker’s reasoning?
o Which of the following would be most important to know when evaluating the
accuracy of the argument above?

• Do not try to skim the passage, read each argument carefully. It is not enough to have a
general idea about the argument; you must be able to analyze it very carefully.

• You must find the conclusion of the argument, which the author claims to have reached.
That most common situations are as follows:
o The conclusion is the last sentence of the passage, often starting by words such
as so, therefore, thus, hence, consequently etc.
o The conclusion is the first sentence of the passage followed by the supporting
evidence.
o Occasionally, the conclusion is not present in the passage; in this case, the
question asks you to identify the conclusion.

• Pay particular attention to signal words such as accordingly, for this reason, hence,
although, but, except, in contrast, nevertheless, unlike etc.

• Eliminating the choices is always the best strategy if you do not know what the correct
answer is. This process will eliminate some obvious wrong choices. And you will be able to
make an educated guess from the remaining ones.

• Every argument is based upon certain assumptions made by the author. If an argument’s
basic premises are sound, the argument is strengthened. If an argument’s basic premises
are flawed, the argument is weakened. In support questions, where you have to decide
about weakening or strengthening the question, pinpoint what the argument assumes. Then
compare that assumption with the answer choices. If the question asks you to find the
choice, which most strengthens the argument, look for the choice that is most in keeping
with the argument’s basic assumption. If the question asks you to choose the choice that
most weakens the argument, look for the answer that casts the most doubt on that
assumption.

• Some logical reasoning questions are essentially mini analytical reasoning questions, so, be
familiar with all of the important logical facts and apply whenever needed. Example
questions with Answers and Explanations

3.2.3 Example Questions with Answers and Explanations

Questions 1-2:
The microwave oven has become a standard appliance in many kitchens, mainly because it offers a
fast way of cooking food. Yet, some homeowners believe that the ovens are still not completely
safe. Microwaves, therefore, should not be a standard appliance until they have been carefully
researched and tested.

1 Which of the following, if true, would most weaken the conclusion of the passage above?

(A) Homeowners, often purchase items despite knowing they may be unsafe.
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(B) Those homeowners in doubt about microwave safety ought not to purchase microwaves.
(C) Research and testing of home appliances seldom reveals safety hazards.
(D) Microwaves are not as dangerous as steam irons, which are used in almost every home.
(E) Homeowners often purchase items that they do not need.

2 Which one of the following, if true, would most strengthen the conclusion of the passage above?

(A) Homeowners often doubt the advertised safety of all new appliances.
(B) Speed of food preparation is not the only concern of today’s homeowner.
(C) Modern homeowners have more free time than ever before.
(D) Food preparation has become almost a science, with more complicated and involved
recipes.
(E) Many microwave ovens have been found to leak radioactive elements.

3 Years ago, a poll concluded that there are more televisions than there are bathtubs in American
homes. No doubt that fact remains today, especially in light of the growing popularity of home
computers. Now, in addition to owning televisions for entertainment, more and more families
are purchasing TV monitors for use with a personal computer. We can safely guess that there
are still many more people staring at a picture tube than singing in the shower.
Which of the following statements can be inferred from this passage?
(A) Personal computers probably cost less than installing a shower or bathtub.
(B) People can wash themselves without a tub or shower, but they cannot watch television
unless they own a television set.
(C) TV monitors will work with personal computers in place of regular computer monitors.
(D) As many computers are sold today as television sets a few years ago.
(E) More television monitors are now used with personal computers than are used to watch
commercial television broadcasts.

4 Some scientists have proposed that, over two hundred million years ago, one giant land mass,
rather than various continents and islands, covers one third of the earth. Long before there
was any human life, and over vast periods of time, islands and continents drifted apart.
Australia was the first to separate, while South America and Africa were late in splitting apart.
Some islands, of course, were formed by volcanoes and were never part of the great land mass.

All the following would support the author’s claim EXCEPT

(A) Many of the plants of the South American rain forests are markedly similar to those of
African rain forests.
(B) Australia has more animals that are not found in any other continent than have several of
the much larger continents.
(C) Volcanic islands like Hawaii have ecosystems very different from those of continental lands
with the same average temperature.
(D) The plants of similar conditions in South America have less in common with those of
Australia than with those of Asia, Africa or Europe.
(E) The primitive languages of Australia are unlike those of Africa, which resembles those of
South America.

5 Every Saturday, Amir has pizza for lunch and then goes to the movies. If the statement above
is true, which of the following statements must also be true?
1 If it is not Saturday, than Amir is not having pizza for lunch and is not going to the movies.
2 If Amir has pizza for lunch and then goes to the movies, it is Saturday.
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3 If Amir has pizza for lunch, but does not go to the movies, it is not a Saturday.

(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 2 only
(E) 2 and 3 only

6 Antifreeze lowers the melting point of any liquid to which it is added so that the liquid will not
freeze in cold weather. It is commonly used to maintain the cooling system in automobile
radiators. Of course, the weather may become so cold that even antifreeze is not effective, but
such a severe climatic condition rarely occurs in well-traveled places.

Which of the following can be deduced from the passage?

(A) Well-traveled places have means of transportation other than automobiles.
(B) Antifreeze does not lower the melting point of certain liquids in extreme conditions.
(C) Severe climatic conditions rarely occur.
(D) It is not often that many travelers who use antifreeze have their cooling system freeze.
(E) Antifreeze raises the melting point of some liquids.

Solutions:
1 The conclusion of the passage is that, because of safety concerns, more research and testing
ought to be done before microwaves become standard household appliances. If, however,
research and testing are ineffective means of discerning safety problems (as choice C says),
then research and testing would be irrelevant. This criticism seriously weakens the conclusion.
So choice C is the correct answer.

2 If many microwave ovens have been found to leak radioactive elements (as choice E says), then
the conclusion that microwaves should not be standard appliances until they are more carefully
researched and tested is further strengthened because more safety concerns need to be
addressed. So, choice E is the correct answer.

3 Though Choices A and B may well be true, they cannot be inferred from the information in the
passage. But choice C can be inferred since, “more and more families are purchasing TV
monitors for use with a personal computer.” TV monitors must work with these computers,
otherwise, people would not buy them for that purpose. Choices D and E may or may not true,
but they are not inferences from the passage, simply additional information. So, the correct
choice is C.

4 If Australia was the first continent to separate, it would follow that its flora and fauna would
develop in isolation over a longer period of time. Similarly, we may expect the plants and animal
of South America and Africa that separated later, to be more alike. Choices A, B, and D support
these ideas. The separately developed islands are different at is also in accord with the passage.
However the languages of all the continents would have developed in isolation, since man did
not evolve until after the break-up of the landmass, and it is surprising that African and South
American languages are similar. Human likeness or differences are irrelevant to the claims of
the passage. So choice E is the correct answer.

5 This logical reasoning question is very easy as soon as you express the given statement
S → (P
symbolically. “If it is Saturday, then Amir has Pizza and goes to Movies” translates as
∧ M). This is equivalent to ~ (P ∧ M) →~ S , which is equivalent to (~ P∨ ~ M) →~ S .
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So if either P or M is false, then S is false. Therefore, 3 is true, neither 1 nor 2 are true. So, the
correct choice is C.

6 Choice D is the correct answer. Since severe climatic conditions rarely occur in well-traveled
places, it is not necessarily true that “It is not often that many travelers who use antifreeze
have their cooling systems freeze.” Choice A mentions other means of transportation, which is
not addressed in the passage. Choice B refers to “certain” liquids.

Verbal Ability

The purpose of the Verbal Test is to evaluate and analyze your English comprehension and
understanding towards the language. The questions will be basically asked to judge the sentence
completion, analogy and critical reading skills. The questions of different types i.e. about sentence
completion and analogy testing will be asked randomly. The questions about the critical reading
however will be asked separately.

4.1 About the Verbal Questions

As already discussed, this section will consist of the following types of questions i.e. sentence
completion, analogy and the critical reading. The detail about each section is as below;

4.1.1 Sentence Completion

The questions that come under this category are provided with various choices. You are asked to
complete the sentences by filling in the blanks with the most suitable choice.
The questions for sentence completion can be related to any of the other areas of study i.e. science,
literature, history, geography etc but the subject matter would not hinder your language abilities.
You are asked to complete the sentence with the use of correct grammar or vocabulary.

These questions try to determine your ability to recognize the correct sentence structure, right
grammar and how you make the correct choice of vocabulary.

Techniques for Sentence Completion

For the sentence completion a few choices are given that could be selected for completing the
sentences. Only one choice is correct out of the several choices. You have to complete the sentence
by selecting the correct choice according to the grammar or vocabulary. For making the right choice
you can benefit from the following techniques;

• After you read the incomplete sentence do not look at the choices. Try to think about the
correct answer yourself. If you think that you have completed the sentence and found the
correct choice you can consult your list of choices. If the answer you thought matches one
of the choices mentioned in the list that is most probably the right choice to be marked. If
it does not match with the choice you can look for a synonym replacement. This tactic is
very helpful in finding the right answer, it prevents you from confusing yourself with the
wrong choices.
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• Do not select the choice hastily. Even if you are satisfied with your choice try to substitute
it with the other choices so that you are more satisfied with your decision. Sometimes the
other choice fits more appropriately to the sentence.

• When you are asked to complete a sentence, which has two spaces to be filled in, try to put
the first word of every choice in the first blank. Note down the choice that you find best.
Now for the second blank try every second choice of all choices. Note the choice that you
think is most appropriate. Check if the two selected choices are matching one of the given
pair of choices. If it does then select it as your correct choice, if not then consider this pair
as a wrong choice and try with the other choices.

• If you find difficulty in making sense out of certain words and you are not very familiar with
them you can try to make a guess with reference to the context of the sentence. Try to
break the word into various parts and analyze its meaning e.g. if you do not know the
meaning of the word “civilization” break it into two i.e. ‘civilize’ and ‘ation’ now you may
know the meaning of civilize and through the term ‘ation’ you can make out that the word
is a noun of civilize. If you find the word unfamiliar with prefixes and suffixes divide the
word into its parts e.g. prerecording. This word consists of both prefix and suffix. You can
break the word like pre-recording. Here you know that pre means before, record means to
store and -ing is a term of continuous tense. So you can find this break up of words quite
helpful in making out the right sense. If none of the technique works try making a guess
with reference to the context.

• When long and complex sentences confuse you then try to break that sentence into smaller
more sentences by rephrasing it. After you divide it compare with the original sentence to
avoid any misinterpretation. If you are satisfied read the smaller sentences to get the idea
more clearly.

Example Questions

1. Multan ___________ a very hot climate.

A. Has
B. Have
C. Has been
D. With
2. One of the least effective ways of sorting information is learning _________ it.
A. Repeat
B. Repeating
C. To repeat
D. how repeat

3. Salman finished__________ two of his published compositions before his twelfth

birthday.
A. Written
B. Writing
C. To write
D. Wrote

4. Sofia __________ collect stamps, but now she has other interests.
A. Used to
B. Was used to
C. Used to be
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D. Using to

5. After passing through a great trauma of her husband’s death, she __________ hard to
achieve mental relaxation.
A. Struggled
B. Struggling
C. Struggle
D. To struggle

6. In partnership with Pakistan, South Korea ____________on Motor way.

A. Helped worked
B. Helping work
C. Helped working
D. To help working

7. We will wait if you __________ go.

A. Wanted to
B. Want
C. Want to
D. Wanting to

8. If I had more time I ____________ checked my paper.

A. Would have
B. Would
C. Would had
D. Will have

9. I thought that he___________ coming today.

A. Has been
B. Is
C. Was
D. Has

10. That professor enjoys teaching and ___________.

A. Writing
B. Written
C. To write
D. Write

11. Just __________the files on my table.

A. Let
B. Leaves
C. Stay
D. Leave

12. Thank you for __________ me your book.

A. Borrowing
B. Lending
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C. Borrowed
D. Had lent

13. ____________ discovery of insulin, it was not possible to treat diabetes.

A. Prior
B. Before to the
C. Prior to the
D. To prior the

14. Distribute the handouts ___________ the candidates.

A. Between
B. Among
C. To
D. In

15. Only _________ were present at the seminar.

A. a few people
B. a little people
C. a few peoples
D. the little people

Answer Key

1. A 9. C
2. C 10. A
3. B 11. D
4. A 12. B
5. A 13. C
6. C 14. B
7. C 15. A
8. A

4.1.2 Analogy Questions

Analogy means similarity in examples or describing likeness between two or more words. These
questions ask the reader to analyze the relationship between two words in a pair and look for
another similar or equivalent pair of words. You are provided with five other pairs of words. You
are expected to match the original pair, which is given in the question with one of the pairs in the
given choices on the bases of similar relationships between them. This exercise or such questions
try to determine your basic understanding towards vocabulary and your ability to recognize the
relationship between words. Some questions may also ask you to select a suitable antonym for a
given word.

Techniques for Analogy Questions

For the analogy questions you can follow the guidelines mentioned below;

• Do not read the choices before you have analyzed the relationship between the pair of
words, yourself. Try to understand the words more appropriately and think on which basis
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the relationship between the words is formed. After you reach a conclusion read the given
choices afterwards to get a proper match with another pair having the same relationship.

• When you find yourself stuck with a word of difficult vocabulary, do not feel confused. Try
to understand its meaning reference to the context or if it is somewhat familiar try to
remember where and when you heard the word before. It can be a great help.

• Sometimes you find that there is more than one pair that fits well to the question and is
appropriate for the choice, give the original pair a little more thought so that you can further
study the relationship between the words and narrow it down to a more distinct one. After
you have been successful in finding a closer relationship you can now scrutinize the two
other pairs that confused you earlier. Repeating the same procedure with these words
would prove useful.
• Do not get caught up by the tricks of the test makers. Sometimes the questions are
provided with very tricky and dodging choices that misguide greatly. Try to think of every
choice more specifically and narrowly.

• If you are familiar with the parts of speech and their nature, it can be beneficial in making
a more sensible choice. Remember if the words in the original pair are a noun and an
adjective, the correct choice you make should also contain the words in the same
grammatical order. Otherwise, your choice is wrong. So, if you are confused with two pairs
and cannot choose the correct choice you can easily look at their grammatical order and
give preference to the one, which matches the original one.

• Exclude the choice from your consideration that you think is incorrect, e.g. the
choices that do not have the same grammatical unit as of the original pair cannot
match the original pair in anyway. Spend more time on considering the more
possible choices.

• You should know about the various kinds of analogies that are more frequently
asked. Some of the common analogy types are as follows;

i. Synonyms
Some words are linked together in a pair which means the same or has a similar
dictionary definition.e.g Pretty- Beautiful

ii. Describing Qualities

Some pairs have some words in which one word describes the other word. Heavy-
Rain

iii. Class and Member

Some pairs have words which are based on class and member basis e.g.
Electronics-Radio

iv. Antonyms
Some pairs consist of the words that are opposite to each other e.g. Love- Hate

v. Describing Intensity
Some pairs consist of the words in which one describes the intensity of the other
e.g.
Smile-Laughter
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vi. Function
In some pairs a word describes the function of the other word e.g.
Pen-Write

vii. Manners
Some words in a speech describe the manners and behavior e.g.
Polite-Speech

viii. Worker-Workplace
Some pairs in a word describe the profession and its workplace e.g. Doctor-Clinic

Example Questions

1. HEIGHT: MOUNTAIN

(A) Depth : Trench

(B) Shade : Tree
(C) Weight : Age
(D) Speed : Highway
(E) Mineral : Mine

2. OBLIVIOUS : AWARENESS

(A) Comatose : Consciousness

(B) Serene : Composure
(C) Erudite : Knowledge
(D) Adroit : Skill
(F) Invigorate : Energy

3. BELLWETHER : BAROMETER

(A) Proselyte : Spark plug

(B) Panhandler : Kill
(C) Embezzler : Abduct
(D) Cynosure : Magnet
(F) Morass : Catalyst

4. ACT : ACTION

(A) Therapy : Thermometer

(B) Oblivion : Obvious
(C) Liturgy : Literature
(D) Image : Imagine
(E) Bowl : Bowdlerize
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5. BIBULOUS : DRINK

(A) Rapacious : Clothing

(B) Gluttonous : Food
(C) Altruistic : Money
(D) Vegetarian : Meat
(E) Controversy : Reconcile

6. SONG : RECITAL

(A) Author : Bibliography

(B) Episode : Series
(C) Coach : Team (D) Dancer : Agile
(E) Poetry : Prose

7. HOUSE : BIG

(A) Home : Live

(B) School : Daily
(C) Water : Cold
(D) Clothes : Socks

8. ANIMAL : MONKEY

(A) Zebra : Giraffe

(B) Stationery: Pencil
(C) Book : Cap
(D) Tree : Wood

9. HEAVEY : LIGHT

(A) Fat : Thin

(B) Stupid : Idiot
(C) Rough : Surface
(D) Beautiful : Diary

Choose the lettered word or phrase that is most nearly opposite in meaning to
the word in capital letters.

10. DETER

(A) Twist
(B) Intimidate
(C) Encourage
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(D) Straighten
(E) Supply

11. INDIGENOUS

(A) Modern
(B) Alien
(C) Ornamental
(D) Natural
(E) Conceal

12. THERAPEUTIC

(A) Curative
(B) Injurious
(C) Medicinal
(D) Practical
(E) Slander

13. QUIZZICAL

(A) Amused
(B) Unequivocal
(C) Contorted
(D) Dissimilar
(E) Lax

14. ANCILLARY

(A) Dependent
(B) Concomitant
(C) Appendix
(D) Primary
(E) Buffet

15. VIRTUOSO

(A) Wicked
(B) Dazzling
(C) Mediocre
(D) Honorable
(E) Bawdy

Answer Key
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1. A 4. D 7. C 10. C 13. B
2. A 5. B 8. B 11. B 14. D
3. A 6. B 9. A 12. B 15. E

4.1.3 Critical Reading Questions

Questions related to critical reading try to judge your reading skills and how you understand and
interpret what you read. The paper includes a few passages that ask answering questions related
to the passage.

Techniques for Critical Reading Exercises

There are a few techniques related to the Critical Reading Questions that prove to be a
good guideline for solving such questions.

• Do not read the questions before reading the whole passage. Try to skim through
the whole passage and then read the questions to look for a more specific answer.
Read the passage quickly with understanding but do not panic. Try to analyze
what the whole passage is about and what the author really intends to convey.
While reading mark the lines where you think the passage carries the most
important points. These strategies would definitely help you find the answers.

• When you find yourself stuck with a question, do not waste your time on it and go
ahead for the next questions. Sometimes, answering other questions guide you
about the earlier question. But, if you still do not find the answer mark it for doing
in the end more calmly, having enough time to think.

• Try to familiarize yourself with the types of critical reading questions. Once you
know the nature of such questions, you will be able to find the answers more
quickly even when you are reading the passage. The examples of some commonly
asked questions are as follows:

o Central Idea
Mostly, questions are asked to explain the central idea or main theme of the whole
passage, which analyzes how you skim through it. Sometimes, the opening and
closing lines can give you a better clue about answering such questions
properly.

o Specific Details
Sometimes to analyze your scanning abilities you are asked to answer some
specific details about the passage. Such questions are about ‘when’, ‘where’,
‘which’ and ‘who’. You can get the answers of this kind of questions from the
area of the passage which you marked in the first reading, where you think the
most important and informational remarks of the author lies.

o Making Inferences
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Most of the questions ask you to infer from the passages, making your opinion
about what is said in the paragraph, implying meaning and making your own
point of view. These questions try to assess your judgment; you must be clear
in your mind about what the author is referring to and then make your own
opinion according to your understanding and comprehension. Read and think
about all the choices and analyze each of it logically according to your
comprehension rather than the author’s point of view.

o Meaning in Context
Some selected words from the passage are pointed out to explain them with
reference to the context to check your reading comprehension. Sometimes the
word that describes something in a dictionary portrays it the other way when
it appears in the context. The test tries to judge your ability to make sense of
the word in the context.

o Author’s Approach
Some questions ask you to explain the mood in which the author is writing whether
it is sarcastic, humorous, witty, sad etc. When you are asked questions like
these you can look for certain expressions, words, phrases or exclamations,
which describe the tone, mood or style of the author. The feelings of the writer
are mostly exhibited through choice of words. While answering these questions
read the message carefully observing particularly the use of words.

o Title Selection
Some passages ask for selecting a title that best suits the passage. Remember
that the chosen title should not be narrowly or broadly selected. Try to avoid
choosing those titles that describes only one or two paragraphs but the one,
which is applicable to the whole passage and portrays it best.

Example Questions

Passage I:

We are profoundly ignorant about the origins of language and have to content ourselves
with more or less plausible speculations. We do not even know for certain when language
arose, but it seems likely that it goes back to the earliest history of man, perhaps half a
million years. We have no direct evidence, but it seems probable that speech arose at
the same time as tool making and the earliest forms of specifically human cooperation.
In the great Ice Ages of the Pleistocene period, our earliest human ancestors established
the Old Stone Age culture; they made flint tools and later tools of bone, ivory, and antler;
they made fire and cooked their food; they hunted big game, often by methods that called
for considerable cooperation and coordination. As their material culture gradually
improved, they became artists and made carvings and engravings on bones and pebbles,
and wonderful paintings of animals on the walls of caves. It is difficult to believe that the
makers of these Paleolithic cultures lacked the power of speech. It is a long step
Admittedly, from the earliest flint weapons to the splendid art of the late Old Stone Age:
the first crude flints date back perhaps to 500,000 B.C., while the finest achievements of
Old Stone Age man are later than 100,000 B.C.; and, in this period, we can envisage a
corresponding development of language, from the most primitive and limited language of
the earliest human groups to a fully developed language in the flowering time of Old Stone
Age culture.
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How did language arise in the first place? There are many theories about this, based on
various types of indirect evidence, such as the language of children, the language of
primitive societies, the kinds of changes that have taken place in languages in the course
of recorded history, the behavior of higher animals like chimpanzees, and the behavior of
people suffering from speech defects. These types of evidence may provide us with useful
pointers, but they all suffer from limitations, and must be treated with caution. When we
consider the language of children, we have to remember that their situations are quite
different from that of our earliest human ancestors, because the child is growing up in an
environment where there is already a fully developed language, and is surrounded by
adults who use that language and are teaching it to him. For example, it has been shown
that the earliest words used by children are mainly the names of things and people (“Doll,”
“Spoon,” “Mummy”): but, this does not prove that the earliest words of primitive man
were also the names of things and people. When the child learns the name of an object,
he may then use it to express his wishes or demands: “Doll!: often means “Give me my
doll!” Or “I’ve dropped my doll: pick it up for me!”; the child is using language to get
things done, and it is almost an accident of adult teaching that the words used to formulate
the child’s demands are mainly nouns, instead of words like “Bring!”’ “Pick up!”; and so
on.

1 The main idea of this excerpt is

A. to provide evidence of the origin of language.
B. to present the need for language.
C. to discuss how early man communicated.
D. to present the culture of early man.
E. to narrate the story of English.
F.
2 Theories of the origin of language include all of the following EXCEPT
A. Changes occurring through the years.
B. The need to communicate.
C. Language of children.
D. The first man’s extensive vocabulary.
E. Communication among primitive men.

3 The purpose of the discussion of the word, “Doll,” is intended to A.

Trace the evolution of a noun.
B. Support the fact that naming things is most important.
C. Indicate how adults teach language to children.
D. Show the evolution of many meanings for one word. E. Evince man’s
multiple uses of single words

4 The implication of the author regarding the early elements of language is that
A. There were specific real steps followed to develop our language.
B. Care must be exercised when exhuming what we consider the roots of
language.
C. We owe a debt of gratitude to the chimpanzee contribution.
D. Adults created language in order to instruct their children.
E. Language was fully developed by primitive man.
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5 If we accept that primitive man existed for a very long period of time without
language, then we may assume that A. Language is not necessary to man’s
existence.
B. Language developed with the developing culture of primitives.
C. Primitives existed in total isolation from one another.
D. Children brought about a need for language.
E. Mankind was not intended to communicate.

6 After a reading of this article, one might infer that A. Society creates problems
with language.
B. Language is for adults to instruct children.
C. Society uses language to improve itself.
D. With the evolution of language came wisdom.
E. Language brings power.

Answer Key

1. A 2. D 3.C 4. B 5. B 6. E
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COMMON QUERIES
Q. How to take NTS Online Test?

You will go through the following screen shots to learn how to take NTS Online test.

Step: 1

This is the first screen named as Candidate Login Screen. You will enter your Candidate ID and
Password provided to you by NTS
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Step: 2
You will see Test Instructions’ Screen after you successfully login. Please read the instructions
carefully to avoid any confusion during the test. After reading the instructions, press Start Test
button on center bottom of the page.

After you click on the Start Test button your test starts and a page appears which shows your first
question of the test. Each question has various choices, if you know the answer you can select the
correct choice for your answer and press Next Question button. You can also add this question in
the Pass Box to answer it at some another stage. You will also find some additional information
about your test on this page. This information includes:

• Total Number of Questions in the Test

• Total Number of Questions Answered by you
• Total Number of Questions in the Pass box to be attempted later
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Step: 3

If you place a question in Pass Box you will notice that the Questions in Pass Box field will
increase by one.
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Step: 4

If you want to answer the questions in Pass Box, simply click on Questions in Pass Box link at
the top. It will take you on the following screen. Now click Answer this Question button for the
question you want to answer.
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Step: 5

You have selected this question from Pass Box now select its answer and proceed for next question.
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Step: 6

You have attempted all questions and now this last screen will show your detailed result.
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Step: 7

Wish You Good Luck with your Test. National

Testing Service

Q. How is NTS Online Test different from paper-based Test?

For the Paper-based Test,

• A pencil, eraser and a sharpener is required to attempt the paper-based test.

• You can make the changes in the answer that you have already marked.
• The announcement of results is delayed than the online tests.
• You have to fill in a separate answer sheet to mark your answers.

Where as for the Online Test,

• No stationery items are required to attempt online test.

• If you want to attempt a question at the end, you can place it in the Pass Box for
attempting later.
• You can not reattempt a question that you have already answered.
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Step: 8
• As soon as you finish the test, the result is displayed on the screen.
• In case of a system failure during the test, you will have to log-in again and the
test will start from the same question where you had left. No information will be
lost while the system was unavailable.
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Q. How Can I Ask for Result Reporting?

Your result is reported to you right after you finish your test. You are given the
certificate fifteen days after the conduct of the test of the last batch. If you still do not
get the result you can Contact Us. You can also visit the website of NTS to check your
result. The final result is sent to you by email.

Q. Is There Any Negative Marking While Scoring?

There is no negative marking for wrong answers. However the negative marking may be
activated if it is required by the allied institute or organization.

Q. What are the Rules and Regulations that apply to me in the Test Center when
taking the Online General Test?

Rules and Regulations:

• If you do not appear with the Identity Card (NIC) on the Test Center, you will not be
allowed to take the test.

• The test will be given on the day and at the scheduled time. You are asked to observe
punctuality. Arriving late at the center may disqualify you from taking the test.

• You are not allowed to bring any testing aids inside the test center. Nothing, except
the original Identity Card is required to be taken along.

• You are not allowed to smoke, eat or drink inside the test center.

• No discussion or any form of communication with the fellow candidates is allowed

during the testing session.

• You will also not be allowed to leave the test center without the permission of the
supervisor.

• Test centers do not have large waiting areas. Friends or relatives who accompany you
to the test center will not be permitted to wait in the test center or contact you while
you are taking the test.

• You will be required to sign the attendance sheet before and after the test session and
any time you leave or enter the premises where the test is being conducted.

• If you need to leave your seat at any time during the test (which shall only be allowed
in case of serious illness), raise your hand and ask the invigilator.
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• Repeated unscheduled breaks will be documented and reported to NTS. NTS reserves
the right to videotape all or any of Testing Sessions and use it to determine any
misconduct, etc.

• If at any time during the test you believe that you have a problem with your test, or
need the Invigilation Staff for any reason, raise your hand to notify the Invigilation
Staff.
NOTE: The rest of the queries regarding the test format, contents and other
procedures have almost the same answers as of the paper based tests, given
above.
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DRILL TESTS
General

Note: The sample papers do not include quantitatively the same number
of questions as there would be in the actual papers. They are merely meant
to provide conceptual guidance to the users or prospective candidates.
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Drill Test I
I Choose the correct answer for each

question and shade the

Quantitative No. Of corresponding CIRCLE on the
10
Section Questions answer sheet

1. The number of degrees through which the hour hand of a clock moves in 2 hours and
12 minutes is

A. 66
B. 72
C. 732
D. 723
E. None of these

A B C D E

2. A cylindrical container has a diameter of 14 inches and a height of 6 inches. Since one
gallon equals 231 cubic inches, the capacity of the tank is approximately

A. 2-2/7 gallons B.
4 gallons
C. 1-1/7 gallons
D. 2-2/7 gallons
E. None of these

A B C D E

3. A train running between two towns arrives at its destination 10 minutes late when it
goes 40 miles per hour and 16 minutes late when it goes 30 miles per hour. The distance
between the two towns is

A. 720 miles
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B. 12 miles C.
8-6/7 miles
D. 12-7/7 miles E.
None of these
A B C D E

4. If the base of a rectangle is increased by 30% and the altitude is decreased by 20%
the area is increased by

A. 25%
B. 10%
C. 5%
D. 1%
E. 4%

A B C D E

5. If the sum of the edges of a cube is 48 inches, the volume of the cube is

A. 512 inches
B. 96 cubic inches
C. 64 cubic inches
D. 698 cubic inches
E. None of these

A B C D E

6. A certain triangle has sides, which are, respectively, 6 inches, 8 inches, and 10 inches
long. A rectangle equal in area to that of the triangle has a width of 3 inches. The Perimeter
of the rectangle, expressed in inches, is

A. 11
B. 16
C. 22
D. 23
E. 24

A B C D E

7. The cube of 1/3 is

A. 3/9
B. 3/27
C. 1/81
D. 1/27
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E. 1/9

A B C D E

8. In general, the sum of the squares of two numbers is greater than twice the product
of the numbers. The pair of numbers for which this generalization is not valid is

A. 8,9
B. 9,9
C.
9,10
D.
9,8
E. 8,10

A B C D E

9. A piece of wire 132 inches long is bent successively in the shape of an equilateral
triangle, a square, a regular hexagon, a circle. The plane surface of the largest area is
included when the wire is bent into the shape of a

A. Circle B.
Square C.
Hexagon
D. Triangle
E. Line

A B C D E

10. If pencils are bought at 35 cents per dozen and sold at 3 for 10 cents the total profit
on 5 1/2 dozen is

A. 25 cents
B. 35 cents
C. 27 1/2 cents
D. 28 1/2 cents
E. 31 1/2 cents

ABCDE
0
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II Choose the correct answer for

each question and shade the No.
Of
ANALYTICAL 20 corresponding CIRCLE in the
Questions
Section answer sheet

For question 1 to 4

Three adults—R, S, and V—will be traveling in a van with five children—F, H, J, L, and M.
The van has a driver's seat and one passenger seat in the front, and two benches behind
the front seats, one bench behind the first. Each bench has room for exactly three people.
Everyone must sit in a seat or on a bench, and seating is subject to the following
restrictions: An adult must sit on each bench. Either R or S must sit in the driver's seat.
J must sit immediately beside M.

1. Which of the following can sit in the front passenger seat?

a
3
b
3
c c. 7
1D 41
E. 4% 13
A B C D E 13
A: F, J, and K 19
B: F, J, and V 35
C: F, S, and V 35
D: H, L, and S 35
E: L, M, and R 35

2. Which of the following groups of three can sit together on a bench?

A B C D E

3. If F sits immediately beside V, which of the following CANNOT be true?

A: J sits immediately beside S.

B: L sits immediately beside V.
C: H sits in the front passenger seat.
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D: F sits on the same bench as H. E:

H sits on the same bench as R.
A B C D E

4. If S sits on a bench that is behind where J is sitting, which of the following must be
true?

A: H sits in a seat or on a bench that is in front of where M is sitting.

B: L sits in a seat or on a bench that is in front of where F is sitting. C:
F sits on the same bench as H.
D: L sits on the same bench as S
E: M sits on the same bench as V.

A B C D E

For question 5 to 9
The principal of a school is forming a committee. There are to be five members: three
teachers, chosen from Mr. J, Ms. K, Ms. L, Mr. M, and Mr. N; and two students, chosen
from O, P, Q, and R. The composition of the committee must conform to the following
conditions: Ms. J will serve only if R is also on the committee. Ms. L will not serve unless
Ms. K and O also serve. Neither Mr. M nor Mr. N will serve without the other. If P serves,
neither Q nor R can serve.

5. Which of the following is an acceptable committee?

A: J, L, M, N, O B:
K, L, N, O, P
C: K, M, N, O, R
D: L, M, N, O, R
E: M, N, O, P, Q

A B C D E

6. How many different committees could include Mr. J and Q?

A: 1 B:
2 C: 3
D: 4
E: 5

A B C D E

7. If Q and R are both on the committee, who else must be on the committee?

A: J
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B: K
C: L
D: M
E: O

A B C D E

8. If M is not on the committee, each of the following must be on the committee EXCEPT

A: J
B: L
C: O
D: Q
E: R

A B C D E
9. In how many different ways can the principal select an acceptable committee?

A: Fewer than 3
B: 3
C: 5
D: 7
E: More than 7

A B C D E

For question 10 to 13

A contractor will build five houses in a certain town on a street that currently has no
houses on it. The contractor will select from seven different models of houses—T, U, V,
W, X, Y, and Z. The town's planning board has placed the following restrictions on the
contractor: No model can, be selected for more than one house. Either model W must be
selected or model Z must be selected, but both cannot be selected. If model Y is selected,
then model V must also be selected. If model U is selected, then model W cannot be
selected.

10. If model U is one of the models selected for the street, then which of the following
models must also be selected?

A: T
B: W
C: X D:
Y
E: Z
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A B C D E

11. If T, U, and X are three of the models selected for the street, then which of the following
must be the other two models selected?

A: V and W
B: V and Y
C: V and Z
D: W and Y
E: Y and Z

A B C D E

12. Which of the following is an acceptable combination of models that can be selected for
the street?

A: T, U, V, X, Y B:
T, U, X, Y, Z
C: T, V, X, Y, Z
D: U, V, W. X, Y
E: V, W, X, Y, Z

A B C D E

13. If model Z is one model not selected for the street, then the other model NOT selected
must be which of the following?

A: T
B: U
C: V
D: W
E: X

A B C D E

For question 14 to 16

Seven children—F, J, K, M, R, S, and T—are eligible to enter a spelling contest. From

these seven, two teams must be formed, a red team and a green team, each team
consisting of exactly three of the children. No child can be selected for more than one
team. Team selection is subject to the following restrictions: If M is on the red team, K
must be selected for the green team. If F is on the red team, R, if selected, must be on
the green team. R cannot be on the same team as S. J cannot be on the same team as
K.
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14. Which of the following can be the three members of the Red team?

A: F, J, and K
B: F, R, and T
C: J, K, and T
D: K, M, and R
E: M, R, and T

A B C D E

15. If M and F are both on the red team, the green team can consist of which of the
following?

A: J, K, and R
B: J, S, and T
C: K, R, and S
D: K, R, and T
E: R, S, and T

A B C D E

16. If M is on the red team, which of the following, if selected, must also be on the red
team?

A: F
B: J
C: R
D: S
E: T

A B C D E

For question 17 to 20

A mail carrier must deliver mail by making a stop at each of six buildings: K, L, M, O, P,
and S. Mail to be delivered are of two types, ordinary mail and priority mail. The delivery
of both types of mail is subject to the following conditions: Regardless of the type of mail
to be delivered, mail to P and mail to S must be delivered before mail to M is delivered.
Regardless of the type of mail to be delivered, mail to L and mail to K must be delivered
before mail to S is delivered. Mail to buildings receiving some priority mail must be
delivered, as far as the above conditions permit, before mail to buildings receiving only
ordinary mail.

17. If K is the only building receiving priority mail, which of the following lists the buildings
in an order, from first through sixth, in which they can receive their mail?
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A: L, K, P, S, O, M B:
L, K, S, P, M, O
C: K, L, P, M, S, O
D: K, P, L, S, O, M
E: O, K, L, P, S, M

A B C D E

18. If L, M, and S are each receiving priority mail, which of the following lists the buildings
in an order, from first to sixth, in which they must receive their mail?

A: K, L, P, S, O, M B:
L, K, O, P, S, M
C: L, K, S, P, M, O
D: M, L, S, P, K, O
E: S, L, M, P, K, O

A B C D E

19. If the sequence of buildings to which mail is delivered is O, P, L, K, S, M and if S is

receiving priority mail, which of the following is a complete and accurate list of buildings
that must also be receiving priority mail?

A: O, L
B: O, P
C: P, L D:
P, M
E: O, P, L, K

A B C D E

20. If only one building is to receive priority mail, and, as a result, O can be no earlier than
fourth in the order of buildings, which of the following must be the building receiving
priority mail that day?

A: K
B: L
C: M
D: P
E: S

A B C D E
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III Choose the correct answer for each

question and shade the

VERBAL No. Of corresponding CIRCLE in the
20
Section Questions answer sheet

Each sentence below has one or two blanks, each blank indicating that
something has been omitted. Beneath the sentence are five lettered words or
sets of words. Choose the word or set of words that, when inserted in the
sentence, best fits the meaning of the sentence as a whole.

1. Florence Nightingale was ___ in the development of modern medicine, ___ such
practices as sanitization of hospital wards and isolation of actively infected
patients.

A. a collaborator…rejecting
B. a maverick…protesting C.
an innovator…initiating
D. a pioneer…criticizing
E. an individualist…standardizing

A B C D E

2. As a journalist who works to overturn erroneous convictions, Griffin Nicholson was

opposed to the court ruling ___ appeals for inmates who might be ___ .

A. barring…culpable B.
curbing…exonerated C.
encouraging…innocent
D. scrutinizing…eligible
E. shielding…esteemed
A B C D E

3. Linda Greenhouse's articles for the New York Times are an outstanding example
of ___, capsulizing prose into a necessarily limited space.

A. Callousne
ss
B. Brevity C.
Intuition
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D.
Propriety
E. Fortitude

A B C D E

4. Roberto Clement was seen as ___ during his life because of both his selflessness
on the baseball field and his humanitarian work in his native Nicaragua.

A. An individualist B.
a grandstander
C. a sybarite
D. an altruist
E. an opportunist

A B C D E

5. His habit of spending more than he earned left him in a state of perpetual-----but
he------------hoping to see a more affluent day.

A. indigence: persevered in B.
confusion: compromised by
C. enervation: retaliated by
D. motion: responded

A B C D E

6. Known for his commitment to numerous worthy causes, the philanthropist

deserved------ for his-----------.
A. recognition: folly B.
blame: hypocrisy
C. reward: modesty
D. credit: altruism

A B C D E

7. You should --------this paragraph in order to make your essay more-----.

A. Delete, succinct B.
Enlarge, redundant C.
Remove, discursive
D. Revise, abstruse

A B C D E
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8. A------glance pays-----attention to details.

A. Furtive: meticulous
B. Cursory: little
C. Cryptic: close
D. Keen: scanty

A B C D E

Each question below consists of a related pair of words or phrases, followed by

five lettered pairs of words or phrases. Select the lettered pair that best
expresses a relationship similar to that expressed in the original pair.

9. TIRADE: ABUSIVE

A. Diatribe: familial
B. Satire: pungent
C. Panegyric: laudatory
D. Eulogy: regretful

A B C D E

10. SOLDIER: REGIMENT

A. Colonel: martinet
B. Dancer: balletomane
C. Singer: chorus
D. Trooper: rifle

A B C D E

11. ASYLUM: SHELTER

A. Harbor: concealment
B. Palisade: display
C. Stronghold: defense
D. Cloister: storage

A B C D E

12. STATIC: MOVEMENT

A. Humdrum: excitement
B. Chronic: timeliness
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C. Ecstatic: decay
D. Diligent: industry

A B C D E

13. INTEREST: FASCINATE

A. Vex: enrage
B. Vindicate: condemn
C. Regret: rue
D. Appall: bother

A B C D E

14. LAUREL: VICTOR

A. Chevrons: army
B. Oscar: movie star
C. Power: glory
D. blue ribbon: cooking

A B C D E

15. PRECEDENT: JUSTIFICATION

A. Kindness: obedience
B. Authority: sanction
C. Usage: submission
D. Tradition: novelty
A B C D E

16. IMPLICATE: COMPLICATE

A. Vitality: inevitable
B. Empathy: sympathy
C. Importune: construct
D. Imply: simplify

A B C D E

17. PERMEATE: RUEFUL

A. Truculent: merciful
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B. Sadden: pitiful
C. Evaporate: mournful
D. Penetrate: sorrowful
A B C D E

18. ENERVATE: STRENGTHEN

A. Aver: attribute
B. Divert: turn
C. Apprise: appraise
D. Stultify: enliven

A B C D E

Read the passages and answer the questions given at the end:

Recent technological advances in manned undersea vehicles have overcome some of the
limitations of divers and diving equipment. Without vehicles, divers often become sluggish
and their mental concentration was limited. Because of undersea pressure that affected
their speech organs, communication among divers was difficult or impossible. But today,
most oceanographers make observations by the means of instruments that are lowered
into the ocean or from samples taken from the water direct observations of the ocean
floor are made not only by divers of more than seven miles and cruise at the depth of
fifteen thousand feet. Radio equipment buoys can be operated by remote control in order
to transmit information back to land based laboratories, including data about water
temperature, current and weather.
Some of mankind’s most serous problems, especially those concerning energy and food,
may be solved with the help of observations made by these undersea vehicles.

19. With what topic is the passage primarily concerned?

A. Recent technological advances.

B. Communication among divers.
C. Direct observation of the ocean floor
D. Undersea vehicles

A B C D E

20. Divers have problems in communicating underwater because?

A. The pressure affected their speech organs B. The

vehicles they used have not been perfected.
C. They did not pronounce clearly
D. The water destroyed their speech organs.
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A B C D E
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Drill Test II
Choose the correct answer for
I
No of each question and shade the
Quantitative 10
Questions corresponding CIRCLE in the
Section
answer sheet

1. A piece of wood 35 feet, 6 inches long was used to make 4 shelves of equal length. The
length of each shelf was

A. 9 feet, 1 1/2 inches

B. 8 feet, 10 1/2 inches
C. 7 feet, 10 1/2 inches
D. 7 feet, 1 1/2 inches
E. 6 feet, 8 1/2 inches

A B C D E

2. The tiles in the floor of a bathroom are 15/16 inch squares. The cement between the tiles
is 1/16 inch. There are 3240 individual tiles in this floor. The area of the floor is

A. 225 sq. yds.

B. 2.5 sq. yds.
C. 250 sq. ft.
D. 22.5 sq. yds
E. 225 sq. ft.

A B C D E
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3. A man bought a TV set that was listed at $160. He was given successive discounts of 20%
and 10%. The price he paid was

A. $129.60 B. $119.60 C. $118.20 D. $115.20

E. $112.00

A B C D E

4. Mr. Jones' income for a year is $15,000. He pays 15% of this in federal taxes and 10% of
the remainder in state taxes. How much is left?

A. $12,750
B. $9,750
C. $14,125 D. $13,500
E. $11,475

A B C D E

5. The radius of a circle which has a circumference equal to the perimeter of a hexagon whose
sides are each 22 inches long is closest in length to which one of the following?

A. 7
B. 21 C. 14 D. 28
E. 24

A B C D E

6. If a, is a multiple of 5 and b = 5a, which of the following could be the value of a + b?

I. 60 II. 100 III. 150

A. I only
B. III only
C. I and III only
D. II and III only
E. None of these

A B C D E

7. Which of the following expressions has the greatest value?

A. 4 × 4 ÷ 4 + 4
B. 4 ÷ 4 × 4 + 4
C. 4 × 4 – 4 × 4 D. 4 ÷ 4 + 4 × 4
E. 2 ÷ 2 + 2 × 2

A B C D E
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8. If (a + 3) / 5 is an integer, what is remainder when ‘a’ is divided by 5?

A. 1 B. 2 C. 3 D. 4
E. 5

A B C D E

9. The integral part of logarithm is called

A. Characteristic
B. Mantissa
C. Solution
D. Root
E. None of these

A B C D E

10. On the y-axis, the x-coordinate is

A. 1
B. ∞
C. zero
D. -∞
E. –1

A B C D E

II Choose the correct answer for

each question and shade the

ANALYTICAL No. Of corresponding CIRCLE in the
20
Section Questions answer sheet

For question 1 to 3

A volunteer uses a truck to pick up donations of unsold food and clothing from stores
and to deliver them to locations where they can be distributed. He drives only along
a certain network of roads. In the network there are two-way roads connecting each
of the following pairs of points: 1 with 2, 1 with 3, 1 with 5, 2 with 6, 3 with 7, 5 with
6, and 6 with 7. There are also one-way roads going from 2 to 4, from 3 to 2, and
from 4 to 3. There are no other roads in the network, and the roads in the network do
not intersect. To make a trip involving pickups and deliveries, the volunteer always
takes a route that for the whole trip passes through the fewest of the points 1 through
7, counting a point twice if the volunteer passes through it twice. The volunteer's
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home is at point 3. Donations can be picked up at a supermarket at point 1, a clothing

store at point 5, and a bakery at point 4. Deliveries can be made as needed to a
tutoring center at point 2, a distribution center at point'6, and a shelter at point 7.

1. If the volunteer starts at the supermarket and next goes to the shelter, the first
intermediate point his route passes through must be

A: 2 B:
3 C: 5
D: 6
E: 7

A B C D E

2. If, starting from home, the volunteer is then to make pickups for the shelter at the
supermarket and the bakery (in either order), the first two intermediate points on
his route, beginning with the first, must be

A: 1 and 2 B:
1 and 3
C: 2 and 1
D: 2 and 4
E: 4 and 2

A B C D E

3. If, starting from the clothing store, the volunteer next is to pick up bread at either
the supermarket or the bakery (whichever stop makes his route go through the
fewest of the points) and then is to go to the shelter, the first two points he reaches
after the clothing store, beginning with the first, must be

A: 1 and 2 B:
1 and 3
C: 4 and 2
D: 6 and 2
E: 6 and 4

A B C D E

For question 4 to 5

There are seven cages next to each other in a zoo. The following is known about the
cages. Each cage has only one animal, which is either a monkey or a bear. There is
a monkey in each of the first and last cages. The cage in the middle has a bear. No
two adjacent cages have bears in them. The bear’s cage in the middle has two monkey
cages on either side. Each of the two other bear cages are between and next to two
monkey cages
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4. How many cages have monkeys in them?

A: 2 B:
3 C: 4
D: 5
E: 6

A B C D E

5. The bear cage in the middle must have

A: No other bear cage to its left B: No

monkey cage on its right. C: A bear
cage to its left and to its right D: Other
bear cages next to it.
E: No monkey cage to its left.

A B C D E

For question 6 to 8

A nursery class in a school has a circular table with eleven seats around it. Five girls
(Kiran, Lado, Maryam, Omera and Parveen) and five boys (Farhan, Ghaus, Haris,
Imdad and Jahangir) are seated around the table. None of the girls are seated in a
seat adjacent to another girl. Kiran sits between Farhan and Ghaus, and next to each
of them. Jahangir does not sit next to Imdad.

6. Which of the following is a possible seating order around the table?

A: Empty seat, Farhan, Kiran, Ghaus, Lado, Omera, Haris, Imdad, Parveen, Jahangir,
and Maryam.
B: Empty seat, Farhan, Kiran, Ghaus, Lado, Jahangir, Parveen, Omera, Imdad,
Maryam, Haris.
C: Empty seat, Farhan, kiran, Ghaus, Omera, Jahangir, Parveen, Imdad, Maryam,
Haris, Lado.
D: Empty seat, Omera, Farhan, Kiran, Ghaus, Lado, Jahangir, Imdad, Parveen, Haris,
Maryam.
E: Empty seat, Maryam, Farhan, Kiran, Ghaus, Lado, Jahangir, Perveen, Imdad,
Omera, Haris.

A B C D E

7. If Lado, Haris, Maryam, Jahangir, and Ghaus are seated in that order, which of the
following is a correct completion of the seating order after Ghaus?
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A : Kiran, Farhan, Omera, Imdad, Parveen, empty seat. B

: Kiran, Farhan, Imdad, Omera, empty seat, Parveen
C : Farhan, Parveen, Kiran, Imdad, Omera, empty seat.
D : Kiran, Farhan, Parveen, Imdad, empty seat, Omera.
E : Kiran, Farhan, Omera, empty seats, Parveen, Imdad.

A B C D E

8. If Jahangir leaves his seat and occupies the empty seat, his new seating position
would be between:

A : Farhan and Kiran

B : Maryam and Ghaus
C : Kiran and Ghaus
D : Imdad and Lado
E : Parveen and Lado

A B C D E

For question 9 to 11
Four telephone operators (Abid, Baqir, Chauhan, and Daud) each have to perform
duties at the telephone exchange on four different days, Thursday through Sunday.
The following is known about their duty schedule: Chauhan has his duty day before
Abid. Daud has his duty day later than Baqir.

9. Which of the following is a possible order of duty days for the four operators?

A: Chauhan, Daud, Abid and Baqir.

B: Daud, Chauhan, Abid, and Baqir.
C: Baqir, Chauhan, Daud and Abid.
D: Abid, Chauhan, Daud and Baqir.
E: Abid, Baqir, Daud and Chauhan.

A B C D E

10. If Chauhan has his duty day on Saturday, who must have his duty day on
Thursday?

A: Either Abid or Daud.

B: Daud
C: Abid
D: Either Baqir or Daud.
E: Baqir.
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A B C D E

11. Each of the following is possible EXCEPT:

A: Chauhan has his duty on Thursday.

B: Baqir has his duty on Thursday.
C: Daud has his duty on Saturday.
D: Baqir has his duty on Sunday E:
Abid has his duty on Sunday.

A B C D E

For question 12 to 13
There are 12 seats facing the blackboard in a classroom, four seats
(A1, A2, A3 & A4) in that order are in row A, the first row from the blackboard.
Immediately behind row A is row B with four seats (B1, B2, B3 & B4) in that order.
Immediately behind row B, is the last row C with four seats (C1, C2, C3 & C4) in that
order. Six students attend the class the following is known about there seating
arrangement: Ejaz sits exactly in front of Comil, Seat A2 is always unoccupied Daud
does not sit next to Farhat, Gharuy sits in seat A4 Hamid does not sit in seat B4 All
the seats in row C always remain empty

12. If Daud sits in seat B3, then Farhat must sit in seat:

A: A3 B:
A1 C:
B4
D: B2
E: C2
A B C D E

13. Suppose that Hamid and Ejaz are sitting in seats A1 and A3 respectively, then it
CANNOT be true that seat:

A: B1 is occupied by Daud.
B: B2 is empty
C: B1 is empty
D: B3 is OCCUPIED BY Comil
E: B4 is empty

A B C D E

For question 14 to 17
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The principal of a school is forming a committee. There are to be five members: three
teachers, chosen from Mr. J, Ms. K, Ms. L, Mr. M, and Mr. N; and two students, chosen
from O, P, Q, and R. The composition of the committee must conform to the following
conditions: Ms. J will serve only if R is also on the committee. Ms. L will not serve
unless Ms. K and O also serve. Neither Mr. M nor Mr. N will serve without the other.
If P serves, neither Q nor R can serve.

14. Which of the following is an acceptable committee?

A: J, L, M, N, O B:
K, L, N, O, P
C: K, M, N, O, R
D: L, M, N, O, R
E: M, N, O, P, Q

A B C D E

15. How many different committees could include Mr. J and Q?

A: 1 B: 2 C: 3
D: 4
E: 5

A B C D E

16. If Q and R are both on the committee, who else must be on the committee? A:
J
B: K
C: L
D: M
E: O

A B C D E

17. In how many different ways can the principal select an acceptable committee? A:
Fewer than 3
B: 3 C:
5
D: 7
E: More than 7

A B C D E

For question 18 to 20
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Three adults—R, S, and V—will be traveling in a van with five children—F, H, J, L, and
M. The van has a driver's seat and one passenger seat in the front, and two benches
behind the front seats, one bench behind the other. Each bench has room for exactly
three people. Everyone must at in a seat or on a bench, and seating is subject to the
following restrictions: An adult must sit on each bench. Either R or S must sit in the
driver's seat. J must sit immediately beside M.

18. Which of the following can sit in the front passenger seat? A:
J
B: L
C: R
D: S
E: V

A B C D E

19. Which of the following groups of three can sit together on a bench?
A: F, J, and M
B: F, J, and V
C: F, S, and V
D: H, L, and S
E: L, M, and R

A B C D E

20. If F sits immediately beside V, which of the following CANNOT be true?

A: J sits immediately beside S.
B: L sits immediately beside V.
C: H sits in the front passenger seat.
D: F sits on the same bench as H.
E: H sits on the same bench as R.

A B C D E
III
Choose the correct answer for each
question and shade the corresponding
VERBAL No. Of
20 CIRCLE in the answer sheet Section
Questions

Each sentence below has one or two blanks; each blank indicates that something
has been omitted. Beneath the sentence are five lettered words or sets of words.
Choose the word or set of words that, when inserted in the sentence, best fits
the meaning of the sentence as a whole.

1. Surprisingly enough, it is more difficult to write about the--------than about the--

and strange.
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A. specific, foreign
B. abstract, prosaic
C. commonplace, exotic
D. simple, routine

A B C D E

2. A-----response is one that is made with----------.

A. stupid, fear B. speedy, alacrity

C. sure, slowness
D. harmful, grimaces

A B C D E

3. A----is a-------.

A. norm, standard B. criterion, mistake

C. discipline, school
D. doctrine, follower

A B C D E

4. It is widely believed that a nuclear war could ____ enough smoke and dust to block
out the sun and freeze the earth.

A. billow B. extinguish
C. generate D.
duplicate
E. decimate

A B C D E

5. Consumption of red meat has ____ because its fat content has become a worrisome
and ____ matter.

A. abated ... dubious

B. skyrocketed ... stressful
C. abounded ... divisive D. stabilized ... newsworthy E. declined ... controversial

A B C D E
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6. It takes ____ character to ____ the extremities of the arctic region.

A. an unflappable ... sustain

B. a dictatorial ... brook C. a Spartan ... negotiate
D. an inimitable ... resist
E. a nomadic ... espouse

A B C D E

7. Consumers refused to buy meat products from the company because of rumors
that the water supply at the meat processing plant was ______; the rumors,
however, were quite ______, with no hard evidence to back them up.

A. uninspected .. reckless
B. contaminated .. unsubstantiated
C. impure .. damaging D. misdirected .. scandalous E. unscrupulous .. vicious
A B C D E

8. Many kinds of harmful viruses are unhindered when passing through different parts
of the host organism; indeed, there are few organic substances which such viruses’
cannot______.

A. undermine
B. disseminate
C. aerate D. exterminate
E. perforate
A B C D E

9. Their conversation was unsettling, for the gravity of their topic contrasted so oddly
with the ______ of their tone

A. uniqueness
B. rapidity
C. lightness
D. precision
E. reverence

A B C D E

10. Throughout the animal kingdom, ____ bigger than the elephant.

A. whale is only the

B. only the whale is
C. is the whale only
D. only whale is the E. whale is only
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A B C D E

Each question below consists of a related pair of words or phrases, followed

by five lettered pairs of words or phrases. Select the lettered pair that best
expresses a relationship similar to that expressed in the original pair.

11. YAWN: BOREDOM ::

A. dream : sleep
B. anger : madness
C. smile : amusement
D. face : expression
E. impatience : rebellion

A B C D E

12. OBSTRUCTION : BUOY ::

A. construction : building
B. boy : girl C. danger : red light
D. iceberg : titanic
E. arise : lay down

A B C D E

13. CONCERT : MUSIC ::

A. performance : artist
B. exhibition : art
C. play : actor
D. operetta : singer E. rock : role

A B C D E

14. TEAMMATE : ADVERSARY ::

A. felon : criminal B. enemy : associate

C. pacifier : agitator
D. winner : loser E.
friend : foe
A B C D E
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For Question 15-20 read the following passage:

A popular theory explaining the evolution of the universe is known as the Big Bang
Model. According to the model at some time between twenty billion years ago, all
present matter and energy were compressed into a small ball only a few kilometers
in diameter. It was, in effect, an atom that contained in the form of pure energy all
of the components of the entire universe. Then, at a moment in time that astronomers
refer to as T = 0, the ball exploded, hurling the energy into space. Expansion occurred.
As the energy cooled most of it became matter in the form of protons, neutrons and
electrons. These original particles combined to form hydrogen and helium and
continued to expand. Matter formed into galaxies with stars and planets.

15. Which sentence best summarizes this passage?

A. The big band theory does not account for the evolution of the universe
B. According to the Big Bang Model, an explosion caused the formation of the
universe
C. The universe is made of hydrogen and helium
D. The universe is more than ten billion years old

A B C D E

16. According to this passage when were the galaxies formed?

A. Ten Billion Years ago

B. Fifteen billion Years ago
C. At T = 0
D. Twenty billion years ago

A B C D E

17. The word “compressed” in the passage could best be replaced by

A. Excited B. Balanced
C. Reduced
D. Controlled

A B C D E

18. It may be inferred that

A. Energy and matter are the same

B. Protons, neutrons, and electrons are not matter
C. Energy may be converted into matter
D. The galaxies stopped expanding as energy cooled
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A B C D E

19. The word “it” in the passage refers to

A. Energy
B. Space
C. Expansion D. Matter

A B C D E

20. The environment before the Big Bang is described as all the following EXCEPT

A. Compressed matter
B. Energy
C. All the components of the universe D. Protons, electrons and neutrons

A B C D E
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Drill Test III

I Choose the correct answer for each
question and shade the
Quantitative No. Of corresponding OVAL in the answer
Section 20 sheet
Questions

1. If the pattern of dots shown above is continued so that each row after Row One
contains 1 dot more than the row immediately above it, which row will contain 12
dots?

A. Seven
B. Eight
C. Nine
D. Ten
E. Twelve

A B C D E

2. Each of Steve's buckets has a capacity of 11 gallons, while each of Mark's buckets
can hold 8 gallons. How much more water in gallons can 7 of Steve's bucket's
hold compared to 7 of Mark's buckets?

A. 3
B. 7
C. 21
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D. 24
E. 56

A B C D E

3. Two integers have a sum of 42 and a difference of 22. The greater of the two
integers is

A. 22
B. 25 C. 28
D. 31
E. 32

A B C D E

4. The average of five numbers is 34. If three of the numbers are 28, 30 and 32,
what is the average of the other two?

A. 40
B. 50
C. 60
D. 70
E. 80

A B C D E

5. In the figure above, what is the value of x?

A. 30
B. 40
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C. 50
D. 80
E. 100

A B C D E

6. In a certain cake, two straight cuts (made along two different radii) succeed in
removing 4/15 of the total cake. What is the central angle in degrees of the piece
cut?

A. 26
B. 60
C. 85 D. 92
E. 96

A B C D E

7. If an equilateral triangle and a square have the same perimeter, what is the ratio
of the length of the sides of the equilateral triangle to the lengths of the sides of
the square?

A. 3:4
B. 4:3
C. 1:4
D. 1:3
E. 3:1
A B C D E

8. If 2 and 4 each divide q without remainder, which of the following must q divide
without remainder.

A. 1
B. 2
C. 4
D. 8
E. It cannot be determined from the information given.

A B C D E

9. The ratio of boys to girls in a certain classroom was 2 : 3. If boys represented

five more than one third of the class, how many people were there in the
classroom?

A. 15
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B. 25
C. 30 D. 45
E. 75

A B C D E

10. Let xy = z, where x,y,z and nonzero numbers. If x is multiplied by 3 and z is

divided by 3, this is equivalent to multiplying y by

A. 1/9
B. 1/3
C. 1
D. 3
E. 9

A B C D E

11. If 5x = 3, then (5x + 3)² =

A. 0
B. 9
C. 18
D. 36
E. 81

A B C D E

12. If the postal charges for a package are 62 cents for the first five ounces and 8
cents for each additional ounce, what is the weight of a package for which the
charges are $1.66? (Assume there are 16 ounces in one pound)

A. 1.05 pounds
B. 1.1 pounds C. 1.125 pounds
D. 1.25 pounds E.
1.5 pounds

A B C D E

13. If m/n = .75, then what is 3m + 2n?

A. 0
B. 8
C. 14
D. 17
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E. 24

A B C D E

14. Which is greater?

Column A Column B

(10/4) / (3/2) * (3/7) (3/4) * (10/7) / (3/2)

A. if the quantity in Column A is greater B. if the quantity in Column B is greater

C. if the two quantities are equal
D. if there is no relationship between these two quantities
E. if the relationship cannot be determined from the information given

A B C D E

15. Which of the following has a graph that is symmetric to the x-axis

A. y=x
B. y = x2 + 3
C. y2 = x
D. y = x3 – x E. y != x

A B C D E

16. The prime factors of 96 are:

A. 2 and 3
B. 6 and 8 C. 2, 3 and 4
D. 8 and 12 E.
3 and 9

A B C D E

17. 8 are what percent of the 6?

A. 1.25
B. 75
C. 125
D. 133.333 E. 150
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A B C D E

18. 2- 3 =

A. -8 B.
8 C. -6
D. -1/8
E. 1/8

A B C D E

19. If x + 1 < 3x + 5, then

A. X > -2
B. x < -2
C. x = 0√√√√
D. x<2
E. x>2

A B C D E

20. Which of the numbers cannot be represented by a repeating decimal?

A. 11/9
B. 23/7
C. √3
D. 4 1/3
E. 2

A B C D E

Choose the correct answer for each

II
question and shade the
Analytical
No. of corresponding CIRCLE in the answer
Reasoning 15
Questions sheet

The office staff of the XYZ Corporation presently consists of three bookkeepers (L, M and N
) and five secretaries (O, P, Q, R and S). Management is planning to open a new office in
another city sending three secretaries and two bookkeepers from the present staff. To do
so they plan to separate certain individuals who do not function well together. The following
guidelines were established to set up the new office:
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(a) Bookkeepers L and N are constantly finding faults with one another therefore should not
be sent together to the new office.
(b) N and P function well alone but not as a team. They should be separated.
(c) O and R have not been on speaking terms for many months. They should not go
together.
(d) Since O and Q have been competing for a promotion, they should not be in one team.
Based on the information given above find the correct answers to the following Questions:

1. If M insists on staying back then how many combinations are possible?

A. 1 B. 2
C. 3
D. None

A B C D E

2. If L is to be moved as one of the bookkeepers, which of the following CANNOT be a possible

working unit?

A. LMOPS
B. LMPQS
C. LMORS
D. LMPRS

A B C D E

3. If N is sent to the new Office which member of the staff CANNOT be sent?

A. O
B. M
C. Q
D. R

A B C D E

4. If O is sent to the new office then which of the following is a possible team?

A. LMOPR
B. MNOQS
C. MNOPS
D. LMOPS

A B C D E

5. If both N and Q are moved to the new office, how many combinations are possible?
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A. 2 B. 3
C. 4
D. 1

A B C D E

6. A map representing countries R, S, W, X, Y and Z is to be drawn. Adjacent countries cannot

have the same color in the map.

The countries adjacent to each other are as follows:

Each of R, S, X and Y is adjacent to W.

X is adjacent to Y.
Each of R and S is adjacent to Z.

If X is the same color as Z then it must be true that

A. W is a different color from any other country.

B. S is a different color from any other country.
C. X is the same color as Y.
D. S is the same color as X.

A B C D E

Two statements, labeled I. & II, follow each of the following questions. The
statements contain certain information. In the questions you do not actually
have to compute an answer, rather you have to decide whether the information
given in the statements I. and II. is sufficient to find a correct answer by using
basic mathematics and every day facts?

7. A long distance runner has just completed running 28 miles. How long did it take him to
finish the journey?

I. His record speed is 8.25 miles per hour.

II. His average speed through the journey was 8
miles per hour.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.
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A B C D E

8. Captain of the national cricket team has to be the most popular member of the team. Who
is the captain of Pakistan’s national cricket team?

I. Waqar is the best player on the team.

II. Waseem is the senior-most member.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

9. In a BCE class at CIIT, 30 boys and 10 girls registered Calculus II. How many boys passed
the course?

I. 5 students could not pass.

II. There were 2 girls who obtained A grade.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

10. A horse ran 100 miles without stopping. What was its average speed in miles per hour? I.
The journey started at 8 PM and ended at 4 AM the following day. II. The horse ran 20
miles per hour for the first 50 miles.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
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D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

11. How much time will computer a need to solve 150 problems? I. The computer needs 50
seconds to solve one problem.
II. Computer never takes more than 60 seconds to solve a problem.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

12. How many pencils does Raheel have?

I. He bought two boxes each containing 10 pencils.

II. He lent two pencils to Khaleel

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

13. In a certain farm there are 47 goats. How many large brown goats are there?

I. 16 of the goats are large.

II. There are 18 brown goats in the farm.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.
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A B C D E

14. Can there be more than 200 pictures in a 60-page book?

I. There is at least one picture in each page.

II. There are no more than 3 pictures in any page.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.
A B C D E

15. If P > Q and R > S, then, P + R > Q + S. Is X > Y?

I. X+A>Y+B
II. A>B

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E
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III. Choose the correct answer for each

question and shade the corresponding

VERBAL CIRCLE in the answer sheet
Section No of
10 Questions

Each sentence below has one or two blanks, each blank indicates that
something has been omitted. Beneath the sentence are five lettered words or
sets of words. Choose the word or set of words that, when inserted in the
sentence, best fits the meaning of the sentence as a whole.

1. Although its publicity has been ___, the film itself is intelligent, well-acted,
handsomely produced and altogether ___

A. tasteless … respectable
B. extensive … moderate
C. sophisticated … moderate
D. risqué … crude
E. perfect … spectacular

A B C D E

2. The Inuit natives of Alaska's North Slope worry that ___ oil exploration might
___their sensitive natural environment.

A. additional…assist
B. current…bolster
C. curtailed…shatter D. unregulated…damage
E. controlled…reassess

A B C D E

3. Ants live in colonies based on ___; each member contributes to the good of all by
actively working with others in performing necessary tasks.

A. Heredity B. Individualism
C. Cooperation
D. Reasoning
E. Instinct
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A B C D E

Each question below consists of a related pair of words or phrases, followed

by five lettered pairs of words or phrases. Select the lettered pair that best
expresses a relationship similar to that expressed in the original pair.

4. STUDYING: LEARNING::
A. running : jumping
B. investigating : discovering
C. reading : writing
D. dancing : swimming
E. talking : listening

A B C D E

5. AFTERNOON : DUSK ::

A. breakfast : dinner B. yesterday : tomorrow

C. Sunday : Saturday
D. night : dawn
E. arise : lay down

A B C D E

6. VIBRATION: SOUND :

A. gravity : pull B. watercolor : paint

C. accident : death
D. worm : reptile
E. arrive : home
A B C D E

7. RUN : RACE ::

A. walk : pogo stick

B. swim : boat
C. fly : kite
D. sink : bottle
E. repair : automobile

A B C D E
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Read the passages and answer the questions asked at its end.

Almost a century ago Alfred Binet, a gifted psychologist, was asked by the French Ministry
of Education to help determine who would experience difficulty in school. Given the influx
of provincials to the capital, along with immigrants of uncertain stock, Parisian officials
believed they needed to know who might not advance smoothly through the system.
Proceeding in an empirical manner, Binet posed many questions to youngsters of different
ages. He ascertained which questions when answered correctly predicted success in
school, and which questions when answered incorrectly foretold school difficulties. The
items that discriminated most clearly between the two groups became, in effect, the first
test of intelligence.

Binet is a hero to many psychologists. He was a keen observer, a careful scholar, an

inventive technologist. Perhaps even more important for his followers, he devised the
instrument that is often considered psychology's greatest success story. Millions of
people who have never heard Binet's name have had aspects of their fate influenced by
instrumentation that the French psychologist inspired. And thousands of
psychometricians — specialists in the measurement of psychological variables — earn
their living courtesy of Binet's invention.

Although it has prevailed over the long run, the psychologist's version of intelligence is
now facing its biggest threat. Many scholars and observers — and even some iconoclastic
psychologists — feel that intelligence is too important to be left to the psychometricians.
Experts are extending the breadth of the concept — proposing much intelligence, including
emotional intelligence and moral intelligence. They are experimenting with new methods
of ascertaining intelligence, including some that avoid tests altogether in favor of direct
measures of brain activity. They are forcing citizens everywhere to confront a number of
questions: What is intelligence? How ought it to be assessed? And how do our notions of
intelligence fit with what we value about human beings? In short, experts are competing
for the "ownership" of intelligence in the next century.

8. According to the passage, which of the following is most similar to the "barometer"
developed by Binet?

A. The S.A.T. or other standardized college admission test.

B. The written portion of a driver's license test.
C. Open tryouts for a varsity athletic team D. An electronic scan of brain-wave
activity.
E. The trivia questions of a game show.
A B C D E

9. The author suggests which of the following about "citizens everywhere"?

A. They do not have a sufficiently accurate definition of intelligence to evaluate

recent scientific developments.
B. They stand to benefit from recent progress in the scientific assessment of
intelligence.
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C. The experiments they are performing with new methods of intelligence

measurement are valuable and interesting.
D. They are at odds with the experts over who should have the right to define
"intelligence."
E. Traditionally they have not given careful consideration to some important
issues concerning intelligence.

A B C D E
10. As used in line # 8, "discriminated" most nearly means

A. equalized B. predetermined C. showed favoritism

D. displayed intolerance E.
distinguished

A B C D E

Drill Test IV
I Choose the correct answer for each

question and shade the

Quantitative No. Of corresponding CIRCLE in the
20
Section Questions answer sheet

1
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1. If the length of BC is twice the length of AC, what are the coordinates of B where
A=(x,y)?

A. (x,2y) B. (-x,2y)
C. (2x,y) D.
(-2x,y)
E. (-2x,2y)

A B C D E

2. The average of five numbers is 34. If three of the numbers are 28, 30 and 32, what
is the average of the other two?
A. 40
B. 50
C. 60
D. 70
E. 80

A B C D E

3. In the figure above, rectangle AEJL has been divided into 8 congruent squares with
each of the 8 squares having an area of 16. What is the length of AE + MF + LG+ AL
+ BK + CJ + DH + EG?

A. 32
B. 44
C. 88
D. 128
E. 176

A B C D E

4. For any positive integer x, #x = x²/3 and &x = 9 /x. which of the following is an
expression for the product of #x and &x?

A. 3x
B. x
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C. 1 D. x3/64 E. 27 x3

A B C D E

5. In a certain town, p gallons of gasoline are needed per month for each car. How long
will q gallons last at this rate given that there are r cars in town?

A. pr/q B. qr/p
C. r/pq
D. q/pr
E. pqr

A B C D E
6. Let xy = z, where x,y,z are nonzero numbers. If x is multiplied by 3 and z is divided
by 3, this is equivalent to multiplying y by

A. 1/9
B. 1/3
C. 1
D. 3
E. 9

A B C D E

7. If x, y, and z are different positive odd integers and x + y + z = 11, what is the
greatest possible value of z?

A. 10
B. 9
C. 8
D. 7
E. 6

A B C D E

8. If the postal charges for a package are 62 cents for the first five ounces and 8 cents
for each additional ounce, what is the weight of a package for which the charges are
$1.66? (Assume there are 16 ounces in one pound)

A. 1.05 pounds
B. 1.1 pounds C. 1.125 pounds
D. 1.25 pounds E.
1.5 pounds

A B C D E
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9. What fraction of two weeks is 24 minutes?

A. 1/120
B. 1/336 C. 1/840 D. 1/2880
E. 1/20160

A B C D E
10. If the vertices of a triangle are at (0,0), (-3, 4) and (3, 4), what is the area of the
triangle?

A. 4
B. 6
C. 12
D. 14
E. 18

A B C D E

11. A water-tank has a base with dimensions 2 feet by 6 feet. If a cube with each side 1
foot is totally immersed in the water, how many inches will the water rise? (12inches
= 1 foot)

A. 1
B. 2
C. 4
D. 8
E. It cannot be determined from the information given

A B C D E
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12. In the figure above, the quadrilateral ABCD is a trapezoid with x = 2. The diameter
of each semicircle is a side of the trapezoid. What is the sum of the lengths of the
four drawn semicircles? (Round to the nearest whole number.)

A. 13
B. 16
C. 19
D. 22
E. 31

A B C D E
13. If n + 3 = n x 3, then n =

A. 0.5
B. 1.5 C. 2 D. 2.5
E. 3
A B C D E

14. If an equilateral triangle and a square have the same perimeter, what is the ratio of
the length of the sides of the equilateral triangle to the lengths of the sides of the
square?

A. 3:4
B. 4:3 C. 1:4
D. 1:3
E. 3:1

A B C D E

15. A restaurant has a special whereby both parents can eat for $20 and each child can
eat for $5. Assuming a family group consists of both parents and at least one child,
what is the maximum number of family groups that could have attended given that
the restaurant took $115?

A. 6
B. 5
C. 4
D. 3
E. 2

A B C D E
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16. Which of the following points lays in the interior of the circle whose radius is 10 and
whose center is at the origin?

A. (-9, 4)
B. (5, -19)
C. (0, -10) D. (10, -1) E. (0,15)

A B C D E

II Choose the correct answer for each

question and shade the

Analytical No. Of corresponding CIRCLE in the answer
15
Reasoning Questions sheet
17. If the perimeter of the rectangle ABCD is 14, what is the perimeter of ∆BCD?

A. 7
B. 12 B A
C. 7 + √29
D. 86 D
E. It cannot be determined from C the
information given.

A B C D E

18. The roots of ax2 + bx + c = 0 are real only if

A. b2 – 4ac ≥ 0 B. b2 – 4ac = 0
C. b2 + 4ac = 0
D. b2 – 4ac < 0
E. b2 – 4bc < 0

A B C D E

19. The two numbers, whose sum is -13 and product -30, are

A. 2, 15
B. 2, -15
C. -3, 10
D. 3, 10
E. -3, -13
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A B C D E

20. Let A = total area of five circles of radius r and let B = total area of three circles of
radius s. If A = B, then r / s =

A. 3/5 B. √3 / √5 C. 3π / 5
D. √(3π) / √5
E. 3π

A B C D E

Two statements labeled I & II, follow each of the following questions. The statements contain certain
information. In the questions you do not actually have to compute an answer, rather you have to
decide whether the information given in the statements I. and II. is sufficient to find a correct answer
by using basic mathematics and every day facts?

1. What day of the week is today?

I. Today is March 25.

II. Akram left Pakistan on Wednesday.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

2. Can any of the four rivers be more than 300 meters wide?

I. The narrowest of the four rivers is 240 meters wide. II.

Average width of the four rivers is 300 meters.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
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D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer

A B C D E

3. If it is raining then there must be clouds. Are there clouds?

I. It is not raining.
II. It rained yesterday.

A. Statement I. ALONE is sufficient but II. ALONE is not sufficient to answer this
question.
B. Statement II. ALONE is sufficient but I. ALONE is not sufficient to answer this
question.
C. Statements I. and II. TOGETHER are sufficient to answer the question but
NEITHER of them is sufficient ALONE.
D. Statements I. and II. COMBINED are NOT sufficient to answer the question and
additional information is needed to find the correct answer.

A B C D E

Read the passage to answer the question 4-5

A map representing countries R, S, W, X, Y and Z is to be drawn. Adjacent countries
cannot have the same color in the map. The countries adjacent to each other are as
follows:
Each of R, S, X and Y is adjacent to W. X
is adjacent to Y.
Each of R and S is adjacent to Z.

4. Which of the following countries can be the same color as W?

A. S B. X
C. Y
D. Z

A B C D E

5. Which of the following is a pair of countries that can be the same color?

A. R and S
B. S and W C.
W and X
D. X and Y
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A B C D E
Questions 6 to 11 depends on the following passage

A college president wishes to select four members of a faculty-student committee as special

representatives to meet with the college's board of trustees.

The faculty-student committee consists of eight members four of which (F, G, H and I) are faculty
members whereas the other four (R, S, T and U) are students.

The president can select any four of the eight committee members as long as the following rules are
observed:

The four representatives must consist of exactly two faculty members and two students.

Either F or G must be one of the representatives but F and G both cannot be the representatives.

If R is a representative then H must also be a representative.

If T is a representative then G cannot be a representative.

6. If T is a representative but H is not a representative then the whole group can be determined
if it were also true that:

A. F is a representative.
B. I is a representative.
C. R is not a representative.
D. U is not a representative.

A B C D E

7. If R is a representative then which of the following CANNOT be a representative?

A. H
B. I
C. S
D. T

A B C D E
8. If G is a representative then which of the following can be the other three representatives?

A. F, S and U
B. H, I and R
C. H, R and S
D. I, R and U

A B C D E
9. If neither S nor U is a representative then which of the following is the pair of facultymember
representatives?

A. F and G
B. F and H
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C. F and I
D. G and H

A B C D E

10. If G, I and S are representatives then which of the following must also be a
representative?

A. H
B. R
C. T
D. U

A B C D E

11. If F and I are representatives then which of the following is not a representative?

A. I
B. S
C. U
D. R

A B C D E

Questions 12 to 14 depends on the following passage

At a congress of the Ruling Party, the seven top party leaders, who are all cabinet
ministers, are seated on a platform in order of rank the Prime Minister being in the center.
The closer a person is to the Prime Minister; the higher is his/her rank. Moreover, a person
sitting on the right of the PM outranks the one sitting equidistant on the left of the PM.
The seven leaders are T, U, V, W, X, Y, and Z.
Y is four places to the left of the Minister of Agriculture, who is two places to the right of
V.

U’s neighbors are T and the Minister of Agriculture.

Z is two places to the left of W.

The Ministers of Education, Mining and Culture are seated together, in order, from left to
right.

The remaining Ministers are those of Social Welfare and Defense.

12. The fifth ranking person in the party hierarchy is:

A. Z, the Minister of Mining B.
Y, the Minister of Culture
C. W, the Prime Minister.
D. X, the minister of Defense.
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A B C D E

13. How many of the seven party leaders outrank the Minister of Education?
A. 3
B. 4
C. 5
D. 6

A B C D E

14. The lowest ranking Minister is

A. Minister of Social Welfare.
B. Minister of Defense.
C. Minister of Education.
D. Minister of Mining.

A B C D E

15. “A meadow in springtime is beautiful, even if no one is there to appreciate it.” This
statement would be a logical opposite to which of the following claims? A. People
will see only what they want to see.
B. Beauty exits only in the eyes of the beholder.
C. Beauty does not depend on seasons.
D. The greatest pleasure available to mankind is the contemplation of
beauty.

A B C D E
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III Choose the correct answer for each

Question and shade the

VERBAL No. Of corresponding CIRCLE in the answer
10
Section Questions sheet

Each sentence below has one or two blanks, each blank indicates that something
has been omitted. Beneath the sentence are five lettered words or sets of words.
Choose the word or set of words that, when inserted in the sentence, best fits
the meaning of the sentence as a whole.

1. Some illnesses such as smallpox, which have been almost eliminated in the United
States are still ____ in many places abroad.
A. discussed
B. prevalent
C. scarce D. unknown
E. hospitalized

A B C D E

2. A recent study indicates that the crime rate in the United States remains ____ and
that one in three households ____ some form of major crime in any year
A. incredible ... witnesses B.
astronomical ... experiences
C. simultaneous ... perpetrates
D. unsuccessful ... initiates
E. defeated ... prosecutes

A B C D E

Each question below consists of a related pair of words or phrases, followed by

five lettered pairs of words or phrases. Select the lettered pair that best
expresses a relationship similar to that expressed in the original pair.

3. SALVAGE : TREASURE
A. settle : argument B.
incorporate : company C.
send : correspondence
D. rescue : victim
E. recycle : newspaper
A B C D E

4. CONTROVERSY : ARBITRATOR
A. peacemaker : conflict
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B. artifact : anthropologist
C. game : referee D. dispute :
mediator
E. disease : pathologist

A B C D E

Read the passages and answer the questions given at its end:

We are profoundly ignorant about the origins of language and have to content ourselves
with more or less plausible speculations. We do not even know for certain when language
arose, but it seems likely that it goes back to the earliest history of man, perhaps half a
million years. We have no direct evidence, but it seems probable that speech arose at
the same time as tool making and the earliest forms of specifically human cooperation.
In the great Ice Ages of the Pleistocene period, our earliest human ancestors established
the Old Stone Age culture; they made flint tools and later tools of bone, ivory, and antler;
they made fire and cooked their food; they hunted big game, often by methods that called
for considerable cooperation and coordination. As their material culture gradually
improved, they became artists and made carvings and engravings on bones and pebbles,
and wonderful paintings of animals on the walls of caves. It is difficult to believe that the
makers of these Paleolithic cultures lacked the power of speech. It is a long step
Admittedly, from the earliest flint weapons to the splendid art of the late Old Stone Age:
the first crude flints date back perhaps to 500,000 B.C., while the finest achievements of
Old Stone Age man are later than 100,000 B.C.; and, in this period, we can envisage a
corresponding development of language, from the most primitive and limited language of
the earliest human groups to a fully developed language in the flowering time of Old Stone
Age culture.

How did language arise in the first place? There are many theories about this, based on
various types of indirect evidence, such as the language of children, the language of
primitive societies, the kinds of changes that have taken place in languages in the course
of recorded history, the behavior of higher animals like chimpanzees, and the behavior of
people suffering from speech defects. These types of evidence may provide us with useful
pointers, but they all suffer from limitations, and must be treated with caution. When we
consider the language of children, we have to remember that their situations are quite
different from that of our earliest human ancestors, because the child is growing up in an
environment where there is already a fully developed language, and is surrounded by
adults who use that language and are teaching it to him. For example, it has been shown
that the earliest words used by children are mainly the names of things and people (“Doll,”
“Spoon,” “Mummy”): but, this does not prove that the earliest words of primitive man
were also the names of things and people. When the child learns the name of an object,
he may then use it to express his wishes or demands: “Doll!: often means “Give me my
doll!” Or “I’ve dropped my doll: pick it up for me!”; the child is using language to get
things done, and it is almost an accident of adult teaching that the words used to formulate
the child’s demands are mainly nouns, instead of words like “Bring!”’ “Pick up!”; and so
on.

5. The main idea of this excerpt is

(A) to provide evidence of the origin of language.
(B) to present the need for language.
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(C) to discuss how early man communicated.

(D) to present the culture of early man.
(E) to narrate the story of English.

A B C D E

6. Theories of the origin of language include all of the following EXCEPT (A)
changes occurring through the years.
(B) the need to communicate.
(C) language of children.
(D) the first man’s extensive vocabulary.
(E) communication among primitive men.

A B C D E

7. The purpose of the discussion of the word, “Doll,” is intended to (A) Trace the
evolution of a noun.
(B) Support the fact that naming things is most important.
(C) Indicate how adults teach language to children.
(D) Show the evolution of many meanings for one word.
(E) Evince man’s multiple uses of single words

A B C D E

8. The implication of the author regarding the early elements of language is that (A)
There were specific real steps followed to develop our language.
(B) Care must be exercised when exhuming what we consider the roots of
language.
(C) We owe a debt of gratitude to the chimpanzee contribution.
(D) Adults created language in order to instruct their children.
(E) Language was fully developed by primitive man.

A B C D E

9. If we accept that primitive man existed for a very long period of time without
language, then we may assume that
(A) language is not necessary to man’s existence.
(B) language developed with the developing culture of primitives.
(C) primitives existed in total isolation from one another.
(D) children brought about a need for language.
(E) mankind was not intended to communicate.

A B C D E

10. After a reading of this article, one might infer that (A) society creates problems with
language.
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(B) language is for adults to instruct children.

(C) society uses language to improve itself.
(D) with the evolution of language came wisdom.
(E) language brings power.

A B C D E

Answer Keys to
Drill Tests
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DRILL TEST I - ANSWER KEY

Section-I Quantitative

1. B C D E
B
2. A B C D E 15. A E
C C D
3. A C D E 16. A
B
C E
4. A B D 17. A B C
B E
5. A D E 18. A
DD E
B B
6. A C D E 19. A C
B C E
7. A E 20. A C
D
C II
D
8. A
E BB
B
9.
D Ve
E Section-I r
B
10. aly D bal
E
A t E 1. A
DDD E
ica 2.
B
A l
A C D
Section- n C Reasoning
B
II 3. A 4. E
C C
B D
D E A
C
C E
1. A
B C E
5. BB DD
2. A D C E
B 6. A B C
3. A B D
7.
E
C
DD E
4. D E C
A 8. A BB
B C
E C E
5. A 9. A DDD
B C D
6. E
C D 10. A D
E
7. A C E 11.
B C D
B E
E A
8. A B C
B E
D
B 12.
9. A C
E C E
D B
B C 13.
10. A E C E
B D
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DRILL TEST II - ANSWER KEY

11. A B D E C E

12. A D 14. A C E

13. A B E
D 15. A C
14. A 16. A C E

C E
17. A
E
18. A

1 E

9.
A

20.

Section-I Quantitative
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DRILL TEST III - ANSWER KEY

C D E
1. A
C D E 15.
B C
2. A B C 16. A E
E B
3. A B C D 17. A B C
C D E E
4. A 18. A D
C
B DE B E
5. A 19. A E
C C
B E B
6. A
C 20. A
D E
D E
7. A
B I rbal
D E C
8. A Section- D
B C E II B E
9. A
1. E
A
10. A aly ical D
t 2. B E
A Reasoning A
n B CC Ve E
3.
Section-
II C D 4. A B DD
C C E
5. B DD
B A
C E
1. A E
6. A B C D
2. B E
D
3. A 7. A C DD
B B
C E
4. A 8. A
B C E
C E
5. A B 9. A BB
DD
C D E
10. A D E
6. A B D E
11. A C E
C B
7. B DD
D E E
C 12. A C
B
8. A DD
B
C 13. A C
B
9. D E
A B
C 14. A
B
DD E
10. A B
B 15. A
11. A D E
B 16. A B
C
12. B
E
C
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DRILL TEST IV - ANSWER KEY

13. A D 17. A E

14. A D E 18. A E
D
19.
D E
20. A
D

E
D E
D
DE
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DRILL TEST V - ANSWER KEY

Section-I Quantitative
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DRILL TEST VI - ANSWER KEY

B C 11. B C D
E
E
1. A B D
E
B D 12. AE
2. A B C D
B C 13. AE
3. A B C D
E C D
14. AE
4. C D B C
E
15. AE
B C D

5. A C D E
B Section-III Verbal
6. A C D
B
E
1. B C D E
7. A
C
B
D 2. A B C E
8. A E
C D 3. A B D E
B
9. E 4.
C A C D E
10. B
5. A B C E
E
D
B 6. B C D E
C E
11. A
7. A B D E
B D
E
12. A 8. B C D E
B D
13. A
E 9. A B C
C
B D D
14. A E
C
B 10. A B C
15. A E
C D
B D
16.
C
B D
17. A E

B D
18. A E
nal
II ytic al Reasoning
19.
A C
20. A
E
B
Section- D
E
B C
1. A D
E
B C
2. A E
B C
3. E
B C D
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DRILL TEST VII - ANSWER KEY

4. A 5. B C D E

A C E

B C E
6.
D
B
7. A C E

8. A B E

9.
A

10.
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DRILL TEST IV - ANSWER KEY

Section-I Quantitative

B C B C 11. AE
E
1. A
B C
B C D 12. E
D E
B C
B 13. AE
D E B D
A
B C 14. AE
D E C D

B C 15. AE
A E

B C D
2. E
C
Section-III Verbal
B
3. E
D 1. A C
4. B
E D E
D
5. B
E B C D
D
6.
B B C E
C E
7. A D
B B C E
C E
8. A D B C D E
C E B C E
9. A D

C E B D E
10. A D
C D E
B E
11. D
C D E
12. A B
C E 2. A
D

13. A B
C E 3. A 4. A
D
14. A B
C
D 5.
15. A C E
D 6. A

C E
D 7. A
A II
naly E 8.
A tic
A

16. al Reasoning
B
9. A
C
17.
D E 10. A B C
B
18. D
E
A B C
19.
E
A B C
20. D

B C E
Section-
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1. A B C D E

2. A
C D E

B
3. A
D E

C
4. A B
E

C E
5.

6. A E

7. A

8. A

9. A

10. A
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SAMPLE TEST
General

Note: The Sample Test does not include quantitatively the same number
of questions as there would be in the actual papers. They are merely meant
to provide conceptual guidance to the users or prospective candidates.

I Choose the correct answer for each

question and shade the

VERBAL No. Of corresponding CIRCLE in the answer
15
Section Questions sheet
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Each sentence below has one or two blanks, each blank indicates that
something has been omitted. Beneath the sentence are five lettered words or
sets of words. Choose the word or set of words that, when inserted in the
sentence, best fits the meaning of the sentence as a whole.

1. Despite the millions of dollars spent on improvements, the telephone system in India
remains ________ and continues to ___________ the citizens who depend upon it.

A. Primitive…inconvenience
B. Bombastic...upset
C. Suspicious...connect
D. Outdated...elate
E. Impartial...vex

2. Unlike the images in symbolist poetry which are often vague and _______ , the
images of surrealist poetry are startlingly ________ and bold.

A. extraneous...furtive
B. trivial...inadvertent
C. obscure...concrete
D. spectacular...pallid
E. symmetrical…virulent

3. A good trial lawyer will argue only what is central to an issue, eliminating
___________ information or anything else that might __________ the client.

A. Seminal...amuse
B. Extraneous...jeopardize
C. Erratic...enhance
D. Prodigious...extol
E. Reprehensible…initiate

4. Pollen grains and spores that are 200 millions old are now being extracted from shale
and are ____________ the theory that the breakup of the continents occurred in
stages; in fact, it seems that the breakups occurred almost __________ .

A. refining...blatantly
B. reshaping...simultaneously
C. countermanding...imperceptibly
D. forging...vicariously
E. supporting...haphazardly

Each question below consists of a related pair of words or phrases, followed by

five lettered pairs of words or phrases. Select the lettered pair that best
expresses a relationship similar to that expressed in the original pair.

5. DETENTION : RELEASE ::
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A. viciousness : attack
B. calamity : repair
C. qualification : employ
D. induction : discharge
E. therapy : confuse

6. PONDEROUS : WEIGHT ::

A. eternal : temporality
B. convincing : decision
C. gargantuan : size
D. ancient : value
E. prototypical : affection

7. FEBRILE : ILLNESS ::

A. tenacious : astonishment
B. juvenile : maturity
C. classic : cultivation
D. eccentric : discrimination
E. delusional : insanity

8. EQUIVOCATION : MEANING ::

A. feint : intention
B. secrecy : stealth
C. geniality : amiability
D. travesty : insight
E. refinement : innovation

Choose the lettered word or phrase that is most nearly opposite in meaning to
the word in capital letters.

9. WHIMSICAL :

A. chivalrous
B. perfect
C. predictable
D. hidden
E. backward

10. REVERE :

A. collide B. succumb
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C. threaten
D. divide
E. despise

11. INURED :

A. authoritative
B. dissolute
C. bereft
D. sensitive
E. taxing

12. ALACRITY :

A. skullduggery
B. reluctance
C. interment
D. bellicosity
E. specificity

Read the passages and answer the questions asked at its end.

Art, like words, is a form of communication. Words, spoken and written, render
accessible to humans of the latest generations all the knowledge discovered by the
experience and reflection, both of preceding generations and of the best and foremost
minds of their own times. Art renders accessible to people of the latest generations all
the feelings experienced by their predecessors, and those already felt by their best and
foremost contemporaries. Just as the evolution of knowledge proceeds by dislodging and
replacing that which is mistaken, so too the evolution of feeling proceeds through art.
Feelings less kind and less necessary for the well-being of humankind are replaced by
others kinder and more essential to that end. This is the purpose of art, and the more
art fulfills that purpose the better the art; the less it fulfills it, the worse the art.

13. The author develops the passage primarily by

A. theory and refutation B. example and generalization

C. comparison and contrast
D. question and answer
E. inference and deduction

14. According to the author, knowledge is

A. evolutionary and emotional

B. cumulative and progressive
C. static and unmoving
D. dynamic and cyclical
E. practical and directionless
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15. According to the passage, all of the following are true EXCEPT:

A. Art is a form of communication.

B. Art helps to refine sensibilities.
C. Art is a repository of experience.
D. Real art can never be bad.
E. Art is a progressive human endeavor.
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II
Choose the correct answer for each
question and shade the
Analytical No. Of
20 corresponding CIRCLE in the
Reasoning Questions answer sheet Section

Questions 16-19 are based on the following.

The Western Derby is a race held annually at Bayshore Racetrack. There are eight
gates at the racetrack, but only seven horses are entered in this race—Julius Caesar,
King's Bounty, Longshot, Man Among Boys, Nocturnal, Odyssey, and Phantom. One of
the gates is left empty. The horses are at the gate, waiting for the race to begin.

Gate 1, on the inside of the racetrack, is occupied.

Phantom is at a gate inside of Nocturnal.
The number of gates separating Julius Caesar and King's Bounty equals the number of
gates separating Longshot and Man among Boys.
Nocturnal and Odyssey are next to each other.

16. If Odyssey is at Gate 2, which of the following must be true?

A. Nocturnal is at the innermost gate.

B. King's Bounty is at the outermost gate.
C. A horse occupies the outermost gate.
D. Phantom is at the innermost gate.
E. The outermost gate is not empty.

17. Which of the following is a possible assignment for the horses, from the inside to
the outside?

A. Phantom, King's Bounty, Julius Caesar, Odyssey, Nocturnal, Man Among Boys,
Longshot, vacant
B. vacant, Phantom, Julius Caesar, Longshot, King's Bounty, Man Among Boys,
Nocturnal, Odyssey
C. Longshot, Man Among Boys, Nocturnal, vacant, Phantom, Odyssey, King's
Bounty, Julius Caesar
D. Julius Caesar, King's Bounty, Longshot, Phantom, vacant, Man Among Boys,
Nocturnal, Odyssey
E. Phantom, Julius Caesar, Nocturnal, vacant, Odyssey, King's Bounty, Longshot,
Man Among Boys
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18. If Julius Caesar is at Gate 6, King's Bounty is at Gate 7, and Odyssey is at Gate 4,
which of the following must be true? I. Longshot is at Gate 1.
II. Nocturnal is at Gate 5.
III. Man Among Boys is at Gate 2. IV.
Gate 8 is vacant.

A. I and II only B. II and III only

C. II and IV only
D. I, II, and III only
E. I, II, III, and IV

19. If Julius Caesar and King's Bounty are at the second and fourth gates, respectively,
all of the following can be true EXCEPT

A. Phantom is at Gate 1
B. Man Among Boys is at Gate 3
C. Longshot is at Gate 6
D. Odyssey is at Gate 7
E. Nocturnal is at Gate 7

20. Studies have shown that families who install smoke detectors and own fire
extinguishers have a reduced risk of losing a child in a house fire. Therefore, no
family who installs smoke detectors and owns a fire extinguisher will lose a child
in a house fire.

Of the following, the best criticism of the argument above is that the argument
does not

A. take into account the possibility of losing a child in a house fire despite all
precautionary measures
B. indicate that fire extinguishers are effective during early stages of a fire
C. cite the fact that smoke detectors have proven to be effective in waking
sleeping children during a house fire
D. differentiate between the two major causes of house fires: cooking and heating
E. take into account that families who buy smoke detectors are also more likely
to purchase fire insurance

21. LSD is a drug known to cause synesthesia, a phenomenon in which sensory input
somehow becomes interchanged in the brain: a person with synesthesia might
smell a symphony, hear sun light, or taste a pinprick. While most cases are drug
induced, some people suffer from synesthesia in various forms since birth.

Which of the following can be most safely inferred from the information above?
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A. Synesthesia is not always a drug-induced phenomenon.

B. Some great artists of this century have been known for their synesthetic
proclivities.
C. LSD is an addictive drug.
D. Synesthesia is rarely bothersome to those who experience it.
E. Synesthesia at birth is a result of mothers who have tried LSD.

22. Palindromes are easier to solve than acrostics, but acrostics are more difficult to
create than palindromes. Rebuses are more difficult to solve than acrostics, yet
rebuses are easier to create than palindromes.
If the above information is true, then it must also be true that

A. acrostics are more difficult to create than rebuses

B. palindromes are more difficult to solve than rebuses
C. rebuses are easier to solve than acrostics
D. acrostics are easier to create than rebuses
E. rebuses are easier to solve than palindromes

Questions 23-25 are based on the following.

A university has a procedure for registering and recording complaints. Due to strict
bureaucratic regulations, the following system of passing complaints must be
observed:

A is the first registrar to receive all incoming complaints.

F is the recorder and final administrator to handle a complaint.
Personnel B, C, D, and E may pass complaints only as follows:
A to B
B to either C or D
C to either B or E
D to C
E to either D or F

23.Which is an acceptable path for a complaint to follow, passing from A?

A. B to C to D to F B. B to D to C to F
C. B to C to E to F
D. B to E to F
E. D to C to F

24.If a complaint is received and is handled by each personnel member only one time,
which of the following could be one of the passes?

A. A to C B. C to B
C. C to F
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D. D to C
E. E to D

25.Between which two personnel may a complaint pass by means of two different
paths without any duplication of passes?

A. B to E
B. C to D
C. C to E
D. D to B
E. E to B

Questions 26-31 are based on the following.

In a baseball field, one team can practice at a time. There are seven teams—the Aces,
the Bears, the Cubs, the Ducks, the Eagles, the Falcons, and the Giants. The baseball
field is open seven evenings a week from Monday to Sunday (Sunday being considered
the last day of the week), and the allocation of practice times is governed by the
following rules:

On any evening, only one team can play.

The Aces must practice on Monday.
The Ducks practice exactly one day before the Falcons practice.
The Falcons practice exactly one day before the Giants practice.
The Cubs and the Bears must practice earlier in the week than the Eagles.

26.The latest day in the week that the Bears can practice is

A. Tuesday B. Wednesday
C. Thursday
D. Friday
E. Saturday

27.If a person went to the baseball field on three consecutive evenings, he or she
could see which of the following teams in the order listed?

A. the Falcons, the Giants, the Cubs

B. the Falcons, the Giants, the Ducks
C. the Aces, the Ducks, the Cubs
D. the Bears, the Cubs, the Falcons
E. the Ducks, the Eagles, the Falcons

28.One week, the Cubs practiced on Wednesday and the Ducks practiced the next
day. That week, the Bears must have practiced on
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A. Monday B. Tuesday
C. Friday
D. Saturday
E. Sunday

29.If the Giants practice on Thursday, the Eagles and the Ducks must practice on
which days, respectively?

A. Sunday and Tuesday

B. Saturday and Tuesday
C. Friday and Wednesday
D. Wednesday and Thursday
E. Tuesday and Monday

30.If the Falcons practice on Saturday, the Eagles must practice on what day?

A. Tuesday
B. Wednesday
C. Thursday
D. Friday
E. Sunday

31.The practice schedule has to adhere to which of the following?

A. The Ducks practice earlier in the week than the Eagles.

B. The Falcons practice on a later day than the Eagles.
C. The Falcons practice earlier in the week than the Giants.
D. The Cubs practice earlier in the week than the Ducks.
E. The Bears practice earlier in the week than the Cubs.

32.Wine, cheese, butter, and raisins are all examples of early techniques to preserve
food. In modern times, food scientists have developed other techniques such as
dehydration, hermetic sealing, and radiation. Of these, radiation is the most
controversial because preliminary studies have shown that radiation alters the
natural chemical bonds in fruits and vegetables. Instead of providing salutary
effects, eating radiated produce may well introduce irritating chemicals into the
body, creating a possible health hazard.

Which of the following, if true, supports the conclusion that eating radiated
produce poses a possible health hazard?
A. Radiation affects only those chemical bonds associated with water, that is,
hydrogen and oxygen.
B. Radiation kills microorganisms that hasten food decay.
C. The radiation-induced bonds are unlike any of those found in non-radiated
produce.
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D. Certain microorganisms, namely those found in yogurt cultures, are essential

for proper digestion.
E. Radiation has no effect on foods preserved by drying.

33.Blue Blood, Inc., is a private blood products company that buys blood only from
qualified donors. To qualify, a person must weigh at least 105 pounds, must not
have taken malaria medication in the last three years, must never have had
hepatitis, and must never have used intravenous drugs. Blue Blood nurses know
that traveling has an effect on the possibilities for blood donation: Everyone who
travels to Malaysia is required to take malaria medication; no one who enters
Singapore can have ever used intravenous drugs; everyone traveling to Gorisimi
gets hepatitis.

Which of the following situations would not automatically disqualify a person from
selling blood to Blue Blood?

A. traveling to Malaysia two years ago

B. having once weighed 110 pounds and now weighing 95 pounds
C. being denied admission to Singapore
D. traveling to Gorisimi five years ago
E. using intravenous drugs that were legal at the time

34.Before marriage, couples should be tested for AIDS and any other sexually
communicable diseases. Negative results will guarantee the health and safe-ness
of their marriage.

Which of the following is an assumption of the argument in the passage above?

A. Current state laws require couples who are planning to get married to be tested
for infectious disease in order to prevent possible health problems in the
future.
B. There are many infectious diseases that can be sexually transmitted from one
individual to another.
C. Fortunately even if a test proves positive for a communicable disease, couples
can still lead healthy marriages by taking the proper precautions.
D. Due to advances in medical research over the years, infectious diseases that
used to be fatal can now be effectively treated.
E. All the diseases detectable through testing have no incubation period and the
results of these tests can immediately indicate whether or not the individual
has the disease.

Question 35 is based on the following.

Nine athletes attend a sports banquet. Three of the athletes—}, K, and L—are varsity
football players; two of the athletes—M and N—are varsity basketball players. The
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other four athletes— O, P, Q, and R—belong to the hockey club. All nine athletes will
be seated at three small tables, each seating three athletes. The athletes must be
seated according to the following rules: O and J do not sit at the same table.

P sits together with at least one of K or M.

There can be at most only one football player at a table.

There can be at most only one basketball player at a table.

35. Suppose just one varsity athlete sits at a certain table, and that athlete happens
to be J. If so, who else sits with J?

A. P, Q
B. P, R
C. Q, R
D. O, Q
E. O, P

Choose the correct answer for

III
No of each question and shade the
Quantitative 15
Questions corresponding CIRCLE in the
Section answer sheet

36.If √y = 9, then y2 - √y =

A. √3-9
B. 0
C. 9-√3
D. 6552
E. 6561

37.If (x+3)/6 = 12/(x+4), what is the positive value of x?

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A. 2 B. 3
C. 5
D. √60
E. 12

38.Cindy wants to paint her office. She can buy three cans of the same-priced paint
and three identical brushes for $21, or she can buy four cans of the same paint
and one brush for $22. How much does a can of paint cost?

A. $2 B. $3 C. $4 D. $5
E. $6

39.Which of the following must be true?

I. (25 - 81) = (5 - 9) (5 + 9) II. 7(9

+ 6) = 7(9) + 7(6)
III. 6 ÷ (3 - 1) = (6 ÷ 3) - (6÷1)

A. I only B. II only
C. III only
D. I and II only
E. I, II, and III

40.The sum of a and 9 - 2a is less than 8. Which of the following is (are) the value(s)
of a?

I. a<-1
II. a< 1
III. a>1

A. I only B. II only
C. III only
D. I and II only
E. I and III only

41.Susan is having a party. At 7:00 P.M., guests begin arriving at a uniform rate of 8
people every 15 minutes. If this pattern continues, how many guests will have
arrived by 9:30 P.M.?

F. 10
G. 20
H. 40
I. 64
J. 80
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42.For positive integers p and q, if p2 + 2q2 = 41, and 2p2 +q2 = 34, then p2 =

A. 2.5
B. 7 C. 3
D. 9
E. 16

43.If a:b is 7:6 and 3b:2c is 2:3, what is c/a ?

A. 14/27
B. 7/9 C. 6/7
D. 9/7
E. 27/14

44.In the figure above, if the radius of the circle is 8, and triangle TRS is inscribed in
the circle, then the length of arc TRS is

A. 16π/3
B. (32 π)/3
C. 16 π
D. (128 π)/3 E. 64 π

45. For developing pictures, XYZ Photo Lab charges a service fee of $3 for every
order it receives in addition to a printing fee. If the order consists of 12 pictures
or less, the printing fee per picture is $0.36. If the order consists of more than
12 pictures, the printing fee per picture is $0.24. What is the total cost per
picture for an order consisting of 30 pictures?
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A. $0.11
B. $0.24
C. $0.34
D. $0.46
E. $3.24

46. Lisa found an easy way to add up a sequence of positive even integers with an
even number of terms. She formed pairs of equal sums by adding the first
integer to the last, the second integer to the next-to-last, and so on. She then
computed the total by adding these equal sums. If the total Lisa obtained was
930, how many terms were there in the sequence of positive even integers if
the sequence started with the number 2?

A. 30
B. 39
C. 40
D. 60
E. 465

47. December is the busiest month at Lamont's Gift Shoppe, where sales in
December are 40 percent higher than average. If sales in February are typically
20 percent lower than average, what is the ratio of February sales to December
sales?

A. 1:2
B. 4:2
C. 4:5
D. 4:7
E. 6:7

48. How many 4-digit numbers are there that consist of only odd digits?

A. 20
B. 625
C. 1,024 D. 4,500
E. 5,000

49. For some integer m, let [m] be defined by the equation {m} = m (1- m). If n +
1 = {n + 1}, then n =

A. -2
B. -1
C. 0 D. 1
E. 2
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50. Box A and box B have 6 cards each. Each card is marked with one integer, 1
through 6. Both boxes can have more than one card with the same integer, but
the sum of all the integers in each box must be 18. Two of the cards in box/1
are 6's and two of the cards in box B are 5's. If one card is drawn from box A
and one from box B, but neither a 6 nor a 5 is drawn, what is the largest
possible sum of the integers on the cards drawn from the two boxes?

A. 3
B. 4
C. 7
D. 8
E. 12