QUANTITATIVE

SECTION
TRAP ANSWERS, BALL­PARKING & POE

1. The original price of an article was reduced by 25 percent. 5. The average (arithmetic mean) of x, y and z is 50. What is
During a special sale, the new price was decreased by the sum of (4x + y), (3y+z) and (3z)?
10 percent. By approximately what percent would the (A) 150
price now have to be increased in order to restore the (B) 200
price of the article to its original amount?
(C) 600
(A) 32.5%
(D) 800
(B) 35%
(E) It can’t be found with info given
(C) 48%
(D) 65% 6. Shruti drives from her apartment to her parents’ house
(E) 67.5% and back. On the trip to her parents’ house she drives at
an average speed of 60 miles per hour. On the return trip,
2. A rectangular wooden crate has inside dimensions 3 Shruti drives at an average speed of 80 miles per hour.
meters by 4 meters by 12 meters. What is the length, in Which of the following is the closest approximation of
meters, of the longest, straight, inflexible rod of negligible Shruti’s average speed, in miles per hour, for the
diameter that can be placed completely within the round trip?
crate? (A) 60
(A) 12 (B) 68.6
(B) 12.6 (C) 70
(C) 13 (D) 71.4
(D) 19 (E) 80
(E) 24

7.
4√80 
3. On Tuesday, Monisha buys an apple pie. She eats 2/5 of  √
the pie that night. On Thursday, she takes out the pie
again and eats 2/5 of what is left. How much of the pie √
still remains uneaten? (A) 
(A) 4/25 √
(B)
(B) 1/5 √
(C) 2
(C) 6/25
(D) 6
(D) 9/25
(E) 36
(E) 3/5

4. If a,b,c and d are prime integers such that 1<a<b<c<d and

abcd = 1430, then what is the value of d?
(A) 3
(B) 9
(C) 11
(D) 13
(E) 22

Page # 173
 8. 10. In the figure given, the area of the square WXYZ
is 400. What is the area of the circle with
centre O?

In the square ABCD, the shaded region is the intersection of two circular
regions centered at B and D respectively. If AB = 10, then what is
the area of the shaded region?
(A) 25(π - 2) (A) 20π
(B) 50 (π - 2) (B) 50π
(C) 25π (C) 75π
(D) 50π (D) 100π
(E) 40π (5 − 2 ) (E) 400π

9. In the figure, O, P and R are the centers of three circles, each with
radius 2. What is the perimeter of the shaded region?
Remember to follow these guidelines:
Double‐check before you choose an answer that was too easy on a
difficult question.

When you get stuck on a tough

question, eliminate the predicable trap
answer
before you guess.
(A) 2π/3
(B) π
(C) 4π/3
(D) 2π
(E) 8π/3

Page # 174
FUNDAMENTALS 6. If 3549 multiplied by an integer x,
results in a perfect square, what is the
smallest possible value of x?
1. How many distinct prime factors (A) 3
between 1 and 100 does 3234 have? (B) 7
(A) One (C) 13
(B) Two (D) 21
(C) Three (E) 39
(D) Four
(E) Five 7. A card game was being played by 3
teams with 3 members each. Each
2. A snail travels a total distance of 220 ft member had to lift a card numbered
during a long winter. If it travels 2.2ft from Ace to 9. A team earned one point
every day over a period of 11 days, for picking up an Ace, 2 for picking up a
what percent of the total distance does card numbered 2 and so on. Scores of 0
it cover in 11 days? were allotted for cards numbered 6, 7,
8 and 9. If no team earned more than 6
points and if a card picked by a team
was not replaced, what is the least
3. 3 + 3 X 3 + 9÷ 3 - 3 X 4 = possible score a team could earn?
(A) -3 (A) 0
(B) 0 (B) 1
(C) 3 (C) 2
(D) 6 (D) 3
(E) 24 (E) 4

4. If p and q are positive integers and 8. If √x = 64, then x3 - x2 =

1+p+q+pq = 14, what is the value of pq? (A) 26 (7)
(A) 3 (B) 28 (24 + 1)
(B) 6 (C) 212 (26 - 1)
(C) 7 (D) 212(224 - 1)
(D) 9 (E) 224 (212 - 1)
(E) 14

5. If 4x+2 - 4x -2 = (255) ( 4y), which of the

following is equal to y? 1 2 4 8
(A) x/255 9. + + + =
13 14 15
(B) x-2 12
2 2 2
2
(C) x-4 − 10

(D) 2x (A) 2
(B) 2 −12
(E) 2x+5
(C) 15 × 2 − 15
(D) 2 × 2 −10
(E) 23 × 2 16

Page # 175
10. At Big Inc, the board of Master Trainers 13. rs = 4 and st = 10
meets once every 60 days, while the Column A Column B
teachers council meets once every 25
days. If a year consists of 300 working 4 10
days, the number of board meetings in r t
a year is what percent less than the
number of council meetings in a year? 14. y < 11
(A) 34
(B) 42 Column A Column B
(C) 58
4 (y + 2) 49
(D) 71
(E) 86

11. The sales of company X in 2000 were 15. w=-z&z≠0

62.5% of its sales in 2008.What is the
percent increase in sales from 2000 to Column A Column B
2008?
(A) 37.5 wz w −z
(B) 40
(C) 60
(D) 62.5
16. p is a positive number.
(E) 166
Column A Column B

(p+p)
12. If -2<a<11 and 3<b<12, then which of 2p
the following is NOT true? 2p
(A) 1 < a + b < 23
(B) - 14 < a - b < 8
(C) - 7 < b - a < 14
(D) 1 < b + a < 23 17. x is an integer and 14 < x < 19
(E) - 24 < ab < 132
Column A Column B

The remainder The remainder

when x is divided when x is divided
by 4 by 5

Page # 176
RATIOS 21. The average life expectancy in three
countries A, B and C was 75, 90 and 80
18. The ratio of men to women in years respectively. The ratio of
Pashupati’s club is 4:7. If there are 52 population in the three countries was
male members in the club and no kids, 4:2:3 respectively. What was the
how many people including women are average life expectancy of the three
there? countries combined?
(A) 52 (A) 75
(B) 78 (B) 80
(C) 91 (C) 81
(D) 143 (D) 92
(E) 195 (E) Can’t find with info given

19. The four directors of a certain company AVERAGE/ RATE, MEAN, MEDIAN
supervised a certain number of
employees each. If the ratio of 22. If Set A = {50, 100, 150, n}, which of the
employees supervised by the directors following could be the median of A?
is 3:5:7:8, which of the following Indicate all such values.
CANNOT be the total number of 75
employees supervised?
(A) 115 115
(B) 92
125
(C) 74
(D) 69 135
(E) 46

23. In 1995 a certain store had 1200 Barbie

20. At a certain college the ratio of Dolls in stock, which had been
freshmen to sophomores is 2:3, and the purchased at $20 each. If 800 of these
ratio of sophomores to juniors is 5:6. If toys were sold for $25 each and the
the ratio of juniors to seniors is 3:5, remaining were sold for $10 each. What
what is the ratio of freshmen to is the overall gain or loss in dollars?
seniors? (A) 4000 gain
(A) 1:3 (B) 4000 loss
(B) 5:9 (C) Nil
(C) 3:5 (D) 2000 gain
(D) 4:7 (E) 2000 loss
(E) 5:6

Page # 177
24. Six students from an institute took a
standardized test. The number of
mistakes committed by five of the 27. The average of p, q and 40 is 20 more
students was 18, 14, 20, 8 and 12. If the than the average of p, q, 40 and 60. What is
sixth student committed x number of the average of p and q?
mistakes, such that the mean number (A) 95
of mistakes per student for the six (B) 190
students equals the median, x could be (C) 220
which of these? (D) 240
Indicate all such values.
(E) 380
6
28. A wholesaler bought 120 watches for
15 $30 each. He sold 50% of the watches
for $20 each, 1/3 at $40 each and the
18
rest for $60 each. What was the
24 wholesaler’s approximate average
profit per radio?
(A) $3
25. A car traveling at a constant speed (B) $5
takes 50 seconds longer to travel a (C) $7
distance of 5 miles than it would take to (D) $9
travel at 72 miles per hour. What is the (E) $10
speed of the car?
29. A tank of capacity 3600 liters can be
(A) 40 filled in 2 hours by a pipe. How long in seconds
(B) 50 will it take the pipe to fill a small tank of capacity 30
(C) 60 liters?
(D) 70
(E) 80

26. The average age of a group of 4 people 30. An automobile averaged 19 miles per
is 32 years. If a fifth person joins the gallon. If it travels 608 kilometers, how
group, the overall average becomes many liters of petrol does it
40. What is the age of the fifth person? consume?(1mile = 1.6 km,1gallon = 3.8 liters)
(A) 54 (A) 20
(B) 60 (B) 30
(C) 66 (C) 76
(D) 72 (D) 80
(E) 80 (E) 135

Page # 178
PLUGGING IN DRILL
BASIC PLUG IN
1. Bashir Corp produces x microprocessor 4. When the integer n is divided by 8, the
chips each month only from April to July remainder is 5. Which of the following is not
and ships 50% of the chips an even number?
manufactured (A) n+3
(B) /2  3.5
every month at the beginning of each
month from August to March. Bashir
Corp incurs a rental cost of $0.20 on
every chip per month from August to (C) n-3
March that is not shipped. In terms of x, (D) 3n+1
what is the total rental cost incurred by (E) 5n+2
Bashir Corp in a year?
(A) 0.80x 5. If n is positive and m is n percent of p,
(B) 1.20x then, in terms of n, p is what percent of
(C) 2.40x m?
(A) 100n
(D) 2.80x
(B) 1/100n
(E) 20x
(C) 1/n
(D) 10/n
(E) 10000/n
2. The juice stall at the circus stocked just
2 brands of orange juice tetra packs;
Brand A cost $ 1 per pack and Brand B
cost $1.50 per pack. Last week, Brand A 6. Yogesh is making a straight fence using
contributed to m% of the stall’s n wickets each 6” wide (n ≥ 2); the distance
revenue, and accounted for n% of the between any two consecutive wickets is 1
sales of juice tetra packs. Which of the foot. What is the length of the fence in feet? (1
following expresses m in terms of n? foot = 12”)
(A) 3  1/2
(A) 100n/ (150 - n )
(B) 200n / (250 - n)
(C) 200n/ (300 - n) (B) 3  2/2
(D) 250n/ (400 - n) (C) 3  1/2
(E) 300n / (500 - n)
(D) 3/2
(E) 3(n+1)/2
3. Sathvika travels p% of the distance
between Adayar and Annanagar at 60
miles per hour and the remaining at 40
miles per hour. In terms of P, what was
Sathvika’s average speed in miles per
hour for the entire trip?
(A) (100 - p) / 2
(B) 50p
(C) (100 + p) / 5p
(D) 600p/ (100 - p)
(E) 12000/ (300 - p)
Page # 179
7. If a, b, c and d are points on a number 10. In Anupama’s pizzeria, one-third of the
line such that a < b < c < d, b is twice as pizzas sold during a day were pepperoni
far from c as from a, and c is twice as and one-fifth of the other pizzas sold
far from b as from d, then what is the were pan pizzas. If p pan pizzas were
c−a sold during the day, how many
value of ? pepperoni pizzas, in terms of p, were
d–b sold?
(A) 1/3 2p
(B) 2/3 (A) 15
(C) 1/2 3p
(D) 1
(B) 5
(E) 3
5p
8. If the Josephites soccer team won a (C) 3
total of c games this season and last 5p
season, and the team won b fewer
games this season than last season, (D) 2
how many games did they win last 15p
season?
(E) 2
b−c
(A) 2
c−b
11. Maya and Kavitha each were paid m
(B) 2 dollars in advance to do a certain job
b+c together. Maya worked on the job for
(C) 2 20 hours and Kavitha worked 4 hours
(D) b+  ⁄2 less than Maya. If Kavitha gave Maya n
dollars of her payment so that they
(E) c + ⁄2 would receive the same hourly wage,
what was the dollar amount in terms of
n that Maya was paid in advance?
9. If n is an odd integer greater than 9, in (A) 4n
terms of n, what would be the smallest (B) 5n
even integer greater than n? (C) 6n
(A) n + 3 (D) 8n
(B) n - 5 (E) 9n
(C) 2n
(D) 5n MUST BE/ COULD BE
(E) n + 1
12. If m is an integer, which of the following
must be odd?
(A) 2m + 2
(B) 6m + 3
(C) 7m + 5
(D) 8m - 4
(E) 12 (m + 2)
Page # 180
13. If x2y2 - 4xy = 12 and xy ≠0, then which a
of the following could be a possible
(A) 2
expression for y?
-2
b
x (B) 2

a+b
3 (C) 2
x
a+2
(D) 2
4
x
(E) b+2
2
6
x 16. To mail a package, the rate is m cents
for the first pound, and n cents for each
additional pound, where m > n. Two
packages weighing 8 pounds and 10
pounds, respectively, can be mailed
separately or combined as one package.
Which method is cheaper, and how
14. a and b are 3 digit positive integers and
much money is saved?
a + b is a 4 digit integer. The tens digit
of integer a is 8 and the tens digit of
(A) Combined, with a saving of m - n cents
integer b >2. If a < b, then which of the
(B) Combined, with a saving of n - m cents
following must be true?
(C) Combined, with a saving of m cents
(D) Separately, with a saving of m - n cents
Indicate all such statements.
(E) Separately, with a saving of n cents
The units digit of a + b is greater than
the units digits of either a or b.

The tens digit of a + b < 9.

The hundreds digit of b is at least 5.

15. If a and b are positive integers such that

a
a - b and are both even integers,
b
which of the following must be an odd
integer?

Page # 181
17. If a, b and x are integers greater than
zero, then which of the following must 20. If x, y and z are non-zero integers, and if
be greater than /  ? x > yz, then which of the following
  statements must be true?
(A)
   Indicate all such statements.
 
(B)
  
 $
(C)
  
&'
%

(D) ! " $
  &%
 # '
(E)
  # $
&1
%'

%' & $

21. If d, e and f are integers such that d is

18. The product of positive integers x, y, divisible by e and f is a factor of e, then
and z is 66. If y is even, x is prime and which of the following must be an
xy = 22, which of the following must be integer?
true?
(A) (e+f)/d
(A) y < x < z
(B) x < z < y
(C) x < y < z (B) (d-e)/f
(D) z < x < y
(E) y < z < x (C) f/de
(D) d/ef

x
19. If __= 1.25, where x and y are positive (E) e/df
y
integers, which of the following
statements CANNOT be true?
(A) xy is an even integer
(B) xy is an odd integer
(C) xy is divisible by 5
(D) x + y is an even integer
(E) x + y is an odd integer

Page # 182
 (A) 2.9%
(B) 3.5%
(C) 5.25%
(D) 7.25%
22. Which of the following inequalities is an
algebraic expression for the shaded part of (E) 12.75%
the number line above?
(A) a ≤ 3
25. On Nirmala’s holiday abroad, her ticket
(B) a ≤ 5 accounted for 50% of her expenses
(C) a − 2 ≤ 3 exclusive of taxes, lodging another 25%,
sightseeing 15% and miscellaneous
(D) a −1 ≤ 4 expenses another 10%. If Nirmala paid
10% taxes on her ticket, 4% taxes on
(E) lodging and 2% taxes on her
a +1≤ 4 miscellaneous expenses, then the total
taxes paid by her accounted for what
percent of her total expenses exclusive
HIDDEN PLUG IN of taxes?

(A) 5.2%
23. Sharada Publishing house circulates 2 (B) 5.8%
magazines on sports: Sports Daily and
(C) 6%
Sports Highlights. 2/3rd of the total
prints comprise The Daily and the rest (D) 6.2%
comprises The Highlights. If the cost of (E) 6.6%
The Highlight is 7/4 times that of a
Daily, then the revenue earned from
the Highlight is what fraction of the
total revenue earned from the sales of 26. The population of City X is 60% of the
these 2 publications? population of City Y. The population of
(A) 5/12 City Y is what percent of the population
of City X?
(B) 7/12
(A) 40%
(C) 7/15
(B) 66 ⅔ %
(D) 8/15
(E) 7/8 (C) 87⅓ %
(D) 112%
24. In City A’s water purifying system, there
are 3 levels of filtering. 30% of the (E) 166⅔ %
impurity is is filtered out in the first
stage itself and rest passes onto the
second screen. At the second level, 50% of
the incident impurities get
obstructed while the third stage blocks
out 85% of the impurities reaching this
stage. Approximately, what percentage
of the water’s impurities remain in City
A’s waters?
Page # 183
27. In 1990, City X’s population comprised
of 40% Hispanics, 13% Blacks, 12% 30. Last year, Anjan Car Rental Company
Asians and the rest Caucasians. In repainted 3/5 of its cars, including 7/10
1998, the City’s overall population had of its station wagons. If 1/6 of the
grown by 8%, and the Hispanic company’s cars were station wagons,
population had grown by 15%. Approximately what percent of the cars that were not
what percent of the City’s population station wagons were repainted last
comprised of Hispanics in 1998? year?
(A) 8% (A) 48⅓%
(B) 14% (B) 50%
(C) 22% (C) 58%
(D) 35% (D) 60%
(E) 42% (E) 72%

28. Of all employees, 3/5th of ABC Corp’s 31. At Pravins University, 3 out of every 5
staff was males. ABC Corp identified an students live in an on-campus
employee as a ‘latecomer’ if he or she dormitory. If one out of every 10
was late on more than 3 occasions in a students who do not live in an on-
month. Last month’s attendance campus dormitory lives in a university-
records showed that 1/6th of the male owned apartment, what fractional part
staff were latecomers. If 1/5th of the of the student body does not live in either
female employees were also an on-campus dormitory or a
latecomers, what was the ratio of university-owned apartment?
latecomers to non-late comers? (A) 7/10
a. 1:11 (B) 1/2
b. 5:41 (C) 9/25
c. 9:22 (D) 3/10
d. 9:41 (E) 7/25
e. 9:50

32. Narayanan Mall’s parking garage has

29. In the recent electoral polls, 15% of the space only for a certain number of cars.
voter-turnout were under the age of 30 If 1/5 of the places are left empty and
and were females. If 50% of the voter 2/5 of the places are used by compact
turnout under the age of 30 were not cars, non-compact cars take up what
females, what percent of the voter fraction of the filled spaces in the
turnout were under the age of 30? garage?
(A) 25% (A) 1/3
(B) 30% (B) 2/5
(C) 45% (C) 1/2
(D) 57% (D) 3/5
(E) 65% (E) 4/5

Page # 184
 33. In a call centre, each worker in the night 37. Jagadeesh was standing in a queue. He
shift takes 3/4 as many calls as each was in the 20th position from the
worker in the day shift. If the night shift beginning and in the 16th position from
has 4/5th as many workers as the day the end. How many people were there
shift, what fraction of all the calls taken in the queue?
by workers in both the shifts did the (A) 33
day shift workers take? (B) 34
(A) 2/5 (C) 35
(B) 3/5 (D) 36
(C) 4/5 (E) 37
(D) 5/8
(E) 15/16 38. Arjun travelled 240 miles at a certain
speed. If he were to increase his speed
34. When x litres of fuel were removed by 20 mph, it would have taken him 2
from a tank which was 5/9 full, the tank hours less to travel the same distance.
was only 3/7 full. In terms of x, what is What was his speed in mph?
the capacity of the tank? (A) 30
(A) 10/9 x (B) 40
(B) 7/3 x (C) 50
(C) 8/3 x (D) 60
(D) 63/8 x (E) 80
(E) 63/35 x

PITA
35. In Anirudhville, 60% of the female
population comprised of married
females. Of these, 3/4 the number had
been married for more than 5 years. Of
the number of women who had been
married for more than 5 years, 3/5
were married for less than 10 years. If
108 women had been married for 10
years or more, how many females did
Anirudhville have?
(A) 100
(B) 300
(C) 600
(D) 900
(E) 1200

36. There are thrice as many boys as girls in

a class. If there are 8 more boys than
girls in the class, how many girls are
there in the class?
(A) 4
(B) 6
(C) 8
(D) 9 Page # 185
(E) 12
39. A certain company agreed to pay 80% 42. Charu’s phone company charges 35
of the health club membership fees of cents each minute of use during peak
each of its employees. During a certain hours and 15 cents each minute of use
year, an employee belonged to a health during non-peak hours. If Charu’s
club, and paid an additional $468 for phone company charged her $7.90 for a
personal training. If the amount that half hour phone call, what is the
the company paid for its part of the number of minutes charged at peak
employee’s health club membership fee is hour rates?
equal to the amount that the (A) 7
employee paid for her part of her (B) 13
health club membership fee plus her (C) 15
personal training, how much was the
(D) 17
health club’s membership fee that
year? (E) 21
(A) $960
(B) $780
(C) $640 43. The sum of x distinct integers greater
(D) $520 than zero is less than 75. What is the
(E) $400 greatest possible value of x?
(A) 8
(B) 9
(C) 10
40. Debashish has a pocket full of quarters,
(D) 11
dimes and nickels. He takes 6 coins out
of his pocket that amount to $0.70. If (E) 12
there are only two denominations of
coins among the 6 coins in Debashish’s
hand, how many nickels is he holding? 44. Each student in a class is to choose an
(A) 2 optional subject. If 1/5 chose math,
(B) 3 1/4chose biology, 1/2 chose history and
(C) 4 the remaining 10 chose psychology,
(D) 5 what is the number of students in the
(E) 6 class?
(A) 80
(B) 110
(C) 160
41. A box contains 20 pens and 33 pencils.
(D) 200
How many pencils must be removed
(E) 400
from the box so that 80 percent of the
items in the box will be pens?
(A) 28
(B) 25
(C) 20
(D) 15
(E) 10

Page # 186
GEOMETRY
1. In right triangle ABC shown, AD = ( 4⁄5 AB
ସ
and AE = (1/3)AC . If the area of triangle ADE

is 8, what is the area of triangle ABC?

(A) π
(B) 2π
(C) 3π
(D) 4π
(E) 5π

4. If the line
(A) 10 y+2−b 2
(B) 15
(C) 20 =m+
(D) 24 x x
(E) 30 is rotated 90°, then the slope of the
rotated line would be
1
(A) m
2. A triangle is obtuse if and only if the
degree measure of one of its angles is −1
(B)
greater than 90. A certain triangle has m
sides of lengths 1, 1 and s. What are all (C) m
values of s for which this triangle is (D) -m
obtuse? (E) m-2
(A) 1 ≤ s ≤ 2
(B) 1 < s < 2
5. Points A (0, 0), B (-2, 4) and C (5, 0) lie
(C) 2≤s≤2
on the XY plane. What is the area of the
(D) 2≤ s <2 polygon enclosed by the lines
(E) 2< s<2 connecting A, B and C?
(A) 10
(B) 15
3. ABCD is a quadrilateral inscribed inside (C) 20
the circle whose center is O and has a (D) 25
diameter of 24 units. If AB||CD and the (E) 30
diagonal BC makes an angle of 30° with the
side AB, what is the length of the
minor arc CD?

Page # 187
6. A certain cube floating in a bucket of 9. Length of Diagonal AC = x
water has between 80 and 85 percent
of its volume below the surface of the
water. If between 12 and 16 cubic
centimeters of the cube’s volume is
above the surface of the water, then
the length of a side of the cube in centimeters is
approximately
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
7. A circle is inscribed in equilateral Column A Column B
triangle ABC such that point D lies on
x 12
the circle and on line segment AC, point
E lies on the circle and on line segment
AB and point F lies on the circle and on
line segment BC. If line segment AB=6, 10. In the figure given, if lines PQ and RS
what is the area of the figure created by intersect such that x > 50, which among
line segments AD, AE and minor arc DE? the following could be a possible value
9 
3 - 4- π (
for y?
3 3√3
(A)(A)
(B) 3 3- π
(C) 6 3- π
(D) 9 3 - 3π
(E) 9 3 - 2π
8. In the figure, DF has a length of 5 2
and angle ACD measures 135°. If the
area of parallelogram ACDF is 75, what
is the area of rectangle ABDE?
(A) 50
(B) 55
(C) 58
(D) 60
(E) 65

(A) 50 2
(B) 100
(C) 75 2
(D) 100 2
(E) 150

Page # 188
 14. If a circle whose radius is 4, has its
centre at (4, 3), then which of the
11. AB and CD are two line segments which following must be true?
lie on the XY plane, such that AB is Indicate all such statements
parallel to the X axis. If CD is a
perpendicular bisector of AB passing X axis is tangent to the circle
through (2, 0), what is the co-ordinate
of B if the co-ordinate of A is (-1, 1)? Y axis is tangent to the circle.
(A) (-1,4)
(B) (2,4) (0, 0) lies inside the circle.
(C) (5,1)
(8,3) lies on the circle
(D) (2,-4)
(E) (-3,-3)

12. A rectangular box has dimensions 4,5,6

units. If the box is filled with small cubes of edges 15. In the figure below AB || CD. If AB = 8
2 units, What is the maximum number of cubes and DC = 5 and if the area of the shaded
that can be placed into the box? rectangular region is 20, what is the
(A) 8 area of the unshaded region?
(B) 9
(C) 10
(D) 12
(E) 15

13. If angle ABC = x°,

Column A Column B

x 135

Page # 189
 (A) 6
(B) 8
16. ABC is an equilateral triangle such that (C) 10 2
AC||XY, AB||YZ and BC||XZ
(D) 6 3
(E) 12

19. A cylinder is placed inside a sphere in such a

way that the axis of cylinder passes through the
centre of the sphere. The volume of the sphere
is 36π. If the radius of the cylinder is two - third
the radius of the sphere, what is the maximum
possible height of the cylinder? (Volume of the
sphere =4/3()

(A) 2
Column A Column B
(B) 5
2 (x + y + z) Perimeter of ∆ABC (C) 2 2
(D) 2 5
(E) 6
17. Triangle ABC has two sides measuring 6
and 3.
20. In the figure, MN || AC. MO is the angle
Column A Column B bisector of angle AMN. What is the
value of x?
Perimeter of ABC 17

18. In the given figure, if all the sides are

equal, what is the length of diagonal
AC, if angle DAB = 60°?

Page # 190
21. ABCD is a parallelogram 24. An ice cube is floating in a glass of
1 1
water with between and of its
6 7
mass above water and the rest
submerged below the water’s surface. The
ratio of the part of the mass above water to
the part of the mass below
water is between
1 1
Column A Column B (A) 5 and
6
Area of ∆ ABC Area of ∆ ABD (B) 1 1
6 and
7
5 5
(C)
6 and
7
22. If the area of the squares ABOF and (D) 6 and 7
OCDE are 16 and 9, then what is the 6 7
perimeter of ABCDEFA? (E) and
7 6

25. The above circle is tangent to the x-axis

and the y-axis at r and s respectively.
The circle has a radius of 1, and is
tangent to AB at point t. AB has a slope
of -1. What are the coordinates of t?

(A) 24
(B) 25
(C) 26
(D) 27
(E) 28

23. If the dimensions of a rectangular crate,

in feet are 5 by 6 by 7, which of the
following CANNOT be the total surface
area, in square feet, of two sides of the
crate?
(A) 60
(A) (1,1)
(B) 70
(C) 77 (B) ( 2, 2)
(D) 84 2 2
(C) (1+ , 1+ )
(E) 90 2 2
(D) (1+ 2, 1+ 2)
(E) (2 2, 2 2 )

Page # 191
26. In the figure, the shaded region ABC is (C) 5
an equilateral triangle inscribed inside a (D) 6
circle whose centre D is the midpoint of (E) 7
the line segment AC. If the area of the
shaded region is 9 3 , what is the area
29. AB is the diameter of a circle that lies in
of the unshaded region enclosed by the
the rectangular coordinate system. If
circle?
the coordinates of point A are (5, 19) and
those of B are (17, 7), what is the sum
of the x and y coordinates of the center
of the circles?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25

30. In the figure given, point P is the center

of the circle and PQRS is a square. If PR
(A) 18π - 9 3
is a diagonal of square PQRS, then the
(B) 9 3 -π length of minor arc RT is what fractional
(C) 27π - 9 3 part of the circumference of the circle?
(D) 36π - 9 3
(E) 243π

27. In a coordinate grid, if the points D(-1, - 1),

E(-1, 1), F(a, 1) and G(a, -1) are the
vertices of a rectangle with a diagonal
length of 2 5 and a > 0, then what is
the value of a?
(A) 3 1
(B) 5 (A) 2
(C) 3 5 1
(B)
(D) 9 4
(E) 7 3 1
(C)
6
1
28. What is the maximum number of points (D)
of intersection of 4 distinct lines?
7
(A) 3 1
(E)
(B) 4 8

Page # 192
 CO­ORDINATE GEOMETRY

Let’s start by revising some basic fundamentals:

• When two points are given and the distance b/w them is asked we can use the distance formula:
*$  $#   %  %2 #  2
( x2 − x 1 ) + ( y 2 − y 1 ) where (x1, y1) and (x2, y2) are the two points.
$x# + $x %#  %
• The mid-point between two given points, say (x 1 , y 1 ) and (x 2 , y 2 ) is given by the formula ( + 1 2 2 , , 2 -
y +y 2
1 2 )
2
./01 4 4
Rise
5 6
• Slope of a line is calculated as the inclination of that line with respect to the horizontal:
.23
= Run
5 6
=

• When two lines are parallel, their slopes are same. When 2 lines are perpendicular, their slopes
are negative reciprocals. (Product of their slopes will be -1)

• Equation of a line is given by the equation: ax + by + c = 0 where slope is –a/b .

Another way of representing the equation of the line is y = mx + b where the
slope is m.
 4
Another way of representing the equation of the line is  =1,

b
where a is the x-intercept and b is the y-intercept.

• x-intercept of a line is the point where the line intersects the x-axis. It’s calculated as -c/a.
Hence y value for any x-intercept will be 0 as x-axis is y = 0. Similarly, y-intercept of a line is the point
where the line intersects the y-axis. It’s calculated as -c/b Hence x value for any y-
intercept will be 0 as y-axis is x = 0.

• The equation of a line passing through the point (a, b) and having a slope m is given by (y-b)=m(x-a)

Page # 193
Some problems based on the above concepts: 5. If the equation of a line is given by
12x - 36y - 18 = 0, what is the y-intercept
of the line?
1. What is the distance between the two points
14 -10 -2 2
,- and - , ?
4 3 4 3 (A) -18
(A) 1 (B) 3
(B) 3 (C) 1/3
(C) 5 (D) 1/2
(E) 3/2
(D) 4√2
(E) √41

5 3 6. If the equation of a line is given by

2. Points P , and Q (2, -2) on the
2 2 5x + 8y - 40 = 0, find its x-intercept?
co-ordinate axis plane. (A) 5
(B) 8
A B (C) -5
Distance from P to origin Distance from Q to origin
(D) -8
3. (E) 5/8
What is the slope of a line passing
through the points (14/4,-10/3) and
( 2⁄4, 2⁄3 ?
7. Find the slope of a line that’s parallel to
(A) 1 the line 6x - 3y + 18 = 0?
(B) 3 (A) -1/2
(C) 5 (B) -2
(C) -6
(D) 4√2
(D) 2
(E) -1 (E) 3

4. If the equation of a line is 2x - 3y - 5 = 0,

what is the slope of the line?
8. Find the slope of a line that’s ⊥to the
(A) 2⁄3
line 6x + 3y - 18 = 0?
(B) 2/3 (A) 1/2
(B) -3
(C) -3/2
ଶ
(C) 2
(D) 3/2 (D) 3
(E) 2/15 (E) 6

Page # 194
9. Which of the following is the equation 13. Which of the following could be the equation of
of a line that is passing through the
point (3, 8) and having a slope of 3? a line that’s having a slope of 7 and x-intercept =-1/7 ?
(A) 3x - y + 21 = 0 (A) 49x - 7y + 7 = 0
(B) 9x + 3y - 51 = 0 (B) 14x - 2y - 7 = 0
(C) 6x - 2y - 32 = 0 (C) 49x + 7y -7 = 0
(D) 3x + y - 16 = 0 (D) 14x - 2y + 7 = 0
(E) 3x - y − 1 = 0 (E) -49x - 7y + 7 = 0

10. What is the y-intercept of the line that 14. Which of the following is the equation
is passing through the points (13,-2) and of a line that is passing through the
having a slope of -1? points (-1, -4) and (1, 2)?
(A) -1 (A) 8x - y - 4 = 0
(B) 11 (B) 2x - y = 0
(C) 15 (C) 6x - 2y - 2 = 0
(D) -13/2 (D) 3x - y + 1 = 0
(E) 2/13 (E) Can’t answer with given info

11. What is the x-intercept of the line that

is passing through the points (-4, 15)
and having a slope of -1?
(A) -4 15. Which of the following could be the
equation of a line that’s parallel to
(B) -11
18x - 72y + 90 = 0 and passing through the
(C) 11 mid point between (-14, 10) and (10,-2)?
(D) 19 (A) 36x - 9y + 108 = 0
(E) -15 (B) 4x - 16y + 48 = 0
(C) x- 4y + 18 = 0
(D) -3x + 12y + 36 = 0
12. Which of the following could be the (E) -7x +28y - 122 = 0
equation of a line that’s having a slope
of -6 and y-intercept = -6?
(A) 6x - 36y = - 6
(B) 24x - 4y = - 6
(C) 96x - 16y = 6
(D) 8x + 48y = 6
(E) 12x + 2y = -12

Page # 195
 16. Which of the following could be the equation of a line that’s perpendicular to 96x - 24y - 72 = 0 and passing

through the midpoint between (-22, 6) and (14, -16)?

(A) 44x - 11y + 121 = 0

(B) 6x + (3y/2) + 63/2 = 0
(C) 8x - 2y + 22 = 0
(D) x + 4y + 24 = 0
(E) x + 4y + 16 = 0

17. Which of the following could be the equation of a line that has x-intercept = 2 and y-intercept = 3?
(A) 4x + 2y - 8 = 0
(B) 3x + 2y - 6 = 0
(C) 2x + 3y + 6 = 0
(D) x - y - 3 = 0
(E) 9x + 6y + 18 = 0

18. If a line has the same value for its x- intercept as its y-intercept = 3, then which of
the following could be the equation of that line?
(A) x + y - 6 = 0
(B) x + y - 3 = 0
(C) 3x + 3y + 9 = 0
(D) x - 2y - 6 = 0
(E) 2x - y - 6 = 0

19. Which of the following could be the equation of a line which is passing through the intersection of the two lines
x - 2y + 3 = 0 and 2x - 2y + 6 = 0 and having a slope of -3?

(A) y = - 3x + 3
(B) y = - 3x - 6
(C) y = -3
(D) y = - 3x - 9
(E) y = - 3x + 6

20. In the rectangular coordinate system line x - y = 0 is the perpendicular bisector of line segment AB and the

X - axis is the perpendicular bisector of segment BC. If the coordinates of point A are (3, 4), what are the
cordinates of point C?

(A) (-4, -3)

(B) (-4, 3)
(C) (3, -4)
(D) (4, -3)
(E) (4, 3)

Page # 196
 CHARTS

Answer questions 1 to 5 based on the two

graphs shown below:

2. Approximately what percent of the hours is spent on

learning in Class?
(A) 20%
(B) 32%
(C) 45%
(D) 65%
(E) 80%

3. The total number of hours spent on learning the subjects At

Home is nearest to which of the following:
(A) The prescribed hours for Math
(B) The In Class hours spent on Math
(C) The sum of the Prescribed hours at home for Physics
and prescribed hours in Class for History
(D) The total hours spent on History
(E) The sum of the Prescribed and actual hours spent
on Physics at home

4. Which of the following accounts for approximately

50% of the total numbers of hours spent in studying all
three subjects?
(A) Physics
(B) Math
(C) History
(D) In Class Math
(E) In Class History

5. If half the number of hours spent in Class is utilized at home,

then the percentage of Math done in Class would be
approximately what percentage of the total number of
hours spent in studying Math?

(A) 33% (B) 50% (C) 66% (D) 75% (E) 80%

1. Which of the following gives as many

hours as those spent on Physics?
Indicate all such values.
hours spent at Home - Math
hours spent in Class - Physics and History
hours spent at Home - Math and History
hours spent In Class - Math and History
hours spent In Class - Math
hours to be spent at home History and Physics
Page # 197
 6. During which year was the addition in reserves as a
percentage of previous years' reserve the highest?
(A) 1992
(B) 1993
(C) 1994
(D) 1995
(E) 1996

7. What was the annual percentage growth in reserves from

1992 to 1996?
(A) 40%
(B) 30%
(C) 20%
(D) 12.5%
(E) 10%

8. Between 1995 and 1996, what was the approximate

percentage increase in the number of shares
outstanding?
(A) 30%
(B) 50%
(C) 70%
(D) 80%
(E) Can’t be determined

9. During 1992, approximately what was the equity of the

Company in Million Dollars?
(A) 1330
(B) 1210
(C) 1120
(D) 1000
(E) Can’t be determined
Note:
(A) Equity + Reserves= No. of shares 10. What was the approximate percentage growth in book
outstanding x Book value value from 1992 to 1995?
(B) Reserves/No of shares outstanding =
(A) 15%
Book value ‐10
(B) 30%
Answer questions 6 to 10 based on the two (C) 45%
graphs shown above: (D) 60%
(E) 75%

Page # 198
 12. Of all the students who are in either
The table below shows the number of junior and
junior or senior year, what percentage
senior students enrolled in various study arts? Write your answer to the nearest
degree programs at a south frontier integer.
university. Data is from the same year (i.e.
the junior and senior classes are made up of
different students)
13. Of all the males in junior and senior
year, what percentage study science?
(A) 29.3%
Degree Junior Year Senior Year (B) 37.1%
Mal Fema Tot Mal Fema Tot (C) 38.2%
e le al e le al (D) 43.6%
Science 137 68 205 87 57 144 (E) 47.9%
Arts 82 142 224 106 123 229
Engineer 67 19 86 35 17 52
ing 14. If next year’s junior class is exactly like
Total 286 229 515 228 197 425 this year’s, but has twice as many
engineering students, by what
percent will the overall enrolment of
Answer questions 11 to 15 based on the graph juniors have increased?
shown above: (A) 10.1%
(B) 12.2%
(C) 14.3%
11. What percent of senior females are enrolled in (D) 16.7%
science? Round of your answer to the nearest tenth place. (E) 100.0%

15. In which group is the ratio of males to

females the greatest?
(A) Junior science majors
(B) Senior engineering majors
(C) Junior arts majors
(D) Senior science majors
(E) Junior engineering majors

Page # 199
The pie charts below represent revenue and 17. What are the manufacturing expenses
expenditure for a company in 2008 expressed as a percentage of the
administration expenses?
(A) 9%
(B) 15%
(C) 40%
(D) 150%
(E) 250%

18. What is the ratio of dollars spent on

facilities to dollars earned from
interest?
(A) 1 : 2
(B) 1 : 1
(C) 2 : 1
(D) 8 : 1
(E) Can’t be determined

19. If the company spent $210,000 on raw

materials, how much did it spend on
advertising in 2008?
(A) $20,000
Answer questions 16 to 19 based on the graph
(B) $40,000
shown above:
(C) $55,000
(D) $80,000
(E) Can’t be determined
16. If the company’s revenue equals the
company’s expenses, and if
manufacturing expenses totalled
$180,000, how much revenue did the
company have from sales?
(A) $165,600
(B) $1,200,000
(C) $1,104,000
(D) $1,000,000
(E) $920,000

Page # 200
 21. There were twice as many private
The graph below shows the percent of flights in Europe in 1985 as compared
commercial and private flights delayed by with 1965. What is the ratio of the
origin. number of private flights delayed in
Europe in 1985 to the number of
private flights delayed in 1965?
(A) 4:6
(B) 1:1
(C) 2:1
(D) 6:1
(E) Not enough information

22. In how many years did the percentage

of private flights delayed exceed the
percentage of commercial flights
delayed, both in Europe and the United
1990
States?
1985 (A) 0
1980 (B) 1
1975 (C) 2
1970 (D) 6
1965 (E) Not enough information

23. If 15,000 private flights were delayed in

the United State in 1990, how many
Answer questions 20 to 23 based on the graph commercial flights were delayed in the
shown above: US in that year?
(A) 3,000
(B) 15,000
20. In which year was the percentage of (C) 30,000
private flights delayed greatest in the (D) 45,000
United States? (E) Not enough information
(A) 1990
(B) 1985
(C) 1980
(D) 1975
(E) 1965

Page # 201
 Answer questions 26 -30 based on the table shown
below:

The table below shows the shipping rates

for Express Parcel Service, Inc.

Shipment Method Ground Air Express

Up to 2 pounds $1.50 $2.25 $6.75

Each additional $0.40 $0.60 $1.15

pound (or fraction)
up to 10 pounds
Each additional $0.25 $0.40 $0.75
pound (or fraction)

Answer questions 24 to 25 based on the table

shown above:

24. How much more does it cost to send a

parcel weighing 16.5 pounds by express
delivery than to send the same parcel
by ground delivery? Write your answer to

the nearest integer .

25. By approximately what percent does the average

air delivery cost per pound
for a 21-pound parcel exceed the average ground
delivery cost per pound for a 28-pound parcel? 26. What was the average rate of warming in the northern
Write your answer to the nearest integer. hemisphere from 1940 to 2000?

(A) 0.4 degrees Celsius per decade

(B) 0.04 degrees Celsius per decade
(C) 0.004 degrees Celsius per decade
(D) 0.0004 degrees Celsius per decade
(E) 0.00004 degrees Celsius per decade

Page # 202
27. What was the widest range in average temperature 29. For how many decades did the CFC concentration and
during the decades between 1940 and 2000, and in average temperature of the southern hemisphere
which hemisphere did it occur? simultaneously decrease?

(A) 0.1 degrees in the southern hemisphere (A) 0

(B) 0.15 degrees in the southern hemisphere (B) 1
(C) 0.2 degrees in the northern hemisphere (C) 2
(D) 0.25 degrees in the northern hemisphere
(D) 3
(E) 0.35 degrees in the southern hemisphere
(E) 4
28. What was the increase in CFC concentration in the
northern hemisphere from 1940 to 2000?
30. What was the CFC concentration in the
(A) 4.5 parts per million
northern hemisphere in 1970?
(B) 5 parts per million
(C) 5.5 parts per million
(A) 2.2 parts per million
(D) 6 parts per million
(B) 2.4 parts per million
(E) 6.5 parts per million
(C) 2.8 parts per million
(D) 3.0 parts per million
(E) 3.5 parts per million

Page # 203
 Use for Questions 31-36

31. Between the months of February 2005 and June 2005, inclusive, approximately what was
Company H’s total revenue from online sales?

A) $50,000,000
B) $130,000,000
C) $162,000,000
D) $204,000,000
E) $354,000,000

32. For the month of 2005 during which Company H’s revenue was greatest, revenue from
online sales was what percent of revenue from all sources?

A) 38%
B) 58%
C) 66%
D) 78%
E) 88%

33. For the month of 2005 during which revenue from online sales was most nearly equal
to revenue from all other sources, what was Company H’s revenue from all sources?

A) $45,000,000
B) $74,000,000
C) $78,000,000
D) $90,000,000
E) $128,000,000

Page # 204
34. For how many months during 2005 did Company H have more than 100 million dollars in revenue?

35. In 2005, the amount of Company H’s revenue from sources other than online sales was greatest in
which of the following months?

A) May
B) June
C) July
D) November
E) December

36. Which of the following is the best approximation of the percent increase in Company H’s revenue
from online sales from August, 2005, to September, 2005?

A) 25%
B) 45%
C) 105%
D) 145%

E) 225%

Page # 205
ARITHMETIC PROGRESSION

Let’s start by revising some basic fundamentals:

• In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers

such that the difference of any two successive members of the sequence is a constant. For
instance, the sequence 3, 5, 7, 9, 11, 13... is an arithmetic progression with common difference
2.

If the initial term of an arithmetic progression is a1 and the common difference of successive members is d, then
the nth term of the sequence is given by:

an = a 1 + (n-1) d

In general, an = ai + (n - i)d

• The sum of the components of an arithmetic progression is called an arithmetic series. The sum of first n
members is given by:
n (a1+ an)
Sn = or, when we substitute formula for an,
2

n [2a + (n − 1 ) d ]
1
Sn =
2

Page # 206
Some problems based on the above concepts:

1. What is the 61st term in the following 5. The number of people who can be
series? {1, 7, 13, …} accommodated in the first row of an
(A) 331 amphitheatre is 12. If the amphitheatre
(B) 360 can accommodate 11 rows of people
(C) 361 and after the first row, each row can
accommodate an additional 8 more
(D) 366
people than the previous row, and for a
(E) 367 particular performance, only three
fourth of the total seats were filled,
how many seats were not filled during
2. In the series given, which term is equal the performance?
to 793? {65, 78, 91, …}
(A) 56 (A) 143
(B) 57 (B) 286
(C) 61 (C) 429
(D) 572
(D) 66
(E) 67 (E) 858

6. The age of a tree is determined by the

no of concentric circles that mark the
3. First the sum of the first 19 terms of the stem when the trunk of the tree is cut.
series {-2, 9, 20 …}? A tall redwood tree was cut whose tree-
(A) 1844 trunk had a 60 feet diameter. If the
innermost circle had a diameter that
(B) 1843
measured 30 inches and the concentric
(C) 1940 circles had a 15 inch gap b/w them, how
(D) 3838 many years old was the tree when it
(E) 3686 was cut?

(A) 23
(B) 24
4. Find the sum of first 50 natural
numbers starting from 11. (C) 46
(A) 1210 (D) 47
(B) 1275 (E) 69
(C) 1500
(D) 1775
(E) 3550

Page # 207
SIMPLE INTEREST & COMPOUND INTEREST

Let’s quickly revise some fundamentals before we move on to problems:

P× t× r
Simple Interest formula: S.I. = where P is principle amount, t is the time period and r is the
100
rate of interest.

Simple Interest is calculated only on the principal, or on that portion of the principal which remains unpaid.
Thus when you're working with simple interest, the yearly return never changes though the amount may
change when the interest is added to the principle.

t×r
Amount for Simple Interest is calculated by: A = P (1+ )
100

Compound Interest: Compound interest is the concept of adding accumulated interest back to the
principal, so that interest is earned on interest from that moment on. Thus when you're working
with compound interest, each year the interest amount is greater than the previous year as the base amount
keeps changing.

r nt
A = P (1 + ) where P is principle amount, r is the rate of interest, n is the number of times
100n
the interest is compounded per year, and t is the time period in years.

Some problems based on these concepts: 2. An investor got $5000 from his parents.
He split the money into 2 parts and
invested them at 4% and 6% rate of
interest calculated annually. He got a
1. A man borrows $4000 at 5% interest total of $265.75 when he combined
and $1000 at 10% interest. What is the interests from the 2 investments.
overall rate of interest?
(A) 5% Column A Column B
(B) 6%
(C) 7.5% Amt (in cents) Amt (in cents)
(D) 8% invested at 4% invested at 6%
(E) 10%

Page # 208
3. If $4000 is invested at 6% annual simple 7. When a certain amount, say $x, is
interest for 4 years, and half of the invested in a bank on compound
amount at the end of 4 years is interest computed annually, the
withdrawn and spent, what is the amount for first and second years is
amount, in dollars, that will be left? $180 and $216 respectively.
(A) 480
(B) 960 Column A Column B
(C) 2480
x 145
(D) 2525
(E) 4960

4. If $2400 is invested at 12.5% simple 8. A particular amount deposited for a

interest calculated annually, how long particular rate of interest compounded
does it take, in years, to double it? annually amounts to Rs. 375 in 4 years
(A) 4 and to Rs. 390 in 5 years. What is the
(B) 8 rate of interest?
(C) 16 (A) 1%
(D) 24 (B) 4%
(E) 25 (C) 5%
(D) 6%
5. An amount of $64000 has to become (E) 7.5%
$.125 million in 3 years when
compound interest is calculated
annually. Find the rate of interest?
(A) 1.25%
(B) 25%
(C) 95% 9. When $400 is invested for 1 yrs at a
rate of 8% compounded semi-annually,
(D) 125%
the interest earned is $x. When $200 is
(E) 2500% invested for 1 yrs at a rate of 10%
compounded quarterly, the interest
6. If $500 is invested at 20% compounded
earned is $y.
annually for 3 years, interest earned in
dollars, is x. If same amount was
invested at the same rate and same Column A Column B
time for simple interest, interest earned in
dollars is y. x y

Column A Column B

x-y 65

Page # 209
STANDARD DEVIATION AND NORMAL DISTRIBUTION

Standard Deviation of a set of data is a measure of dispersion (or the degree of spread) of the data. Standard Deviation
depends on each value in the data.

To compute the standard deviation of a set of values follow these steps.

(a) Find the mean.

(b) Find the difference between the mean and each of the values.
(c) Square each of the differences.
(d) Find the average of the squared differences. (this is called the Variance)
(e) Find the non-negative square root of the average. (This is the Standard Deviation)

Consider a set of numbers. Set A = {1, 3, 5, 7, 9}

The Mean is 5.
The deviations of the numbers from the Mean are: 1 – 5 = – 4, 3 – 5 = –2, 5 – 5 = 0 , 7 – 5 = 2, 9 – 5 = 4.
The average of the squares = [(– 4)2 + (– 2)2 + (0)2 + (2)2 + (4)2] / 5 = 40/5 = 8
The Standard Deviation = √8 = 2.83 (approx)

The minimum possible Standard Deviation of a set of values is 0 (zero). This happens when all the values are equal. For
example, the Standard Deviation of the Set B = {4, 4, 4, 4, 4} is 0.

The smaller the Standard Deviation, the more closely packed are the values around the Mean. The greater the Standard
Deviation, the farther away (more scattered) are the values from the Mean.

Another interesting point to note is that the Standard Deviation is always less than or equal to the maximum deviation.

Page # 210
Just to drive home the concept, let’s take two problems that will illustrate this clearly.

1. Set Alpha = {2, 4, 6, 8} Set Beta = {102,104,106,108}

Column A Column B

SD of set Alpha
SD of set Beta

2. Set Alpha = {2, 4, 6, 8} Set Beta = {1, 4, 6, 9}

Column A Column B

SD of set Alpha SD of set Beta

(Answers: Q1 - C and Q2 - B.)

Sometimes SD comes with the word “Normal Distribution” (ND). So

let us see what ND means.

Consider a set V = {30, 40, 40, 50, 50, 50, 60, 60, and 70}.

When we plot these points in a co-ordinate system such that Y-axis represents the number of occurrences and
X-axis represents the values, by joining these points we will get a bell shaped curve, which roughly looks
as follows:

Page # 211
 30 40 50 60 70

Thus if by plotting the elements of a set we get a bell curve, then that set is said to have a ND.

The bell curve has the following interesting properties.

1. The element corresponding to the highest point on the curve represents the mode of the set.
And since it is a normal distribution the mean, median and mode are all equal. So the central
vertical line represents the mean of the set. In this case the mean is 50.

MEAN=50

2. This bell shaped curve is symmetric about the mean, which means that exactly 50% of the data
will lie on either sides of the mean.

3. In a ND 34% of the data lies between the mean and 1st SD on either sides of the mean,14% data
lies between the 1st SD and the 2nd SD on either sides and 2% data lies between the 2nd SD
and the 3rd SD on either sides. The interval which is formed by the 1st SD on either sides of the
mean is called the first SD interval; similarly the second and third intervals.

Page # 212
In the above figure the gaps between the vertical lines are all equal, which is equal to the SD of the set.

For e.g.: Suppose for a given set mean is 50 and SD is 10 and the values follow ND, then the mean
(middle point) is 50. Since SD is 10 the gaps' width is 10. So the next point towards right which is after 1 SD is 60,
the next point will be 70, and the third SD point will be 80. Likewise, the first point towards left which is after 1 SD
is 40, the next point will be 30, and the third SD point will be 20.

The percentage of items that are above 60 will be 14%+2%=16%

The first SD interval will be 40 to 60.

Page # 213
Let’s do a few problems based on these 5. A collar manufacturer is considering the product of a new
style of collar to attract young men. He took a statistics of
concepts: neck circumference of a typical group of 2000 college
students and observed that it follows a normal
1. Which of the following set has distribution with mean 14.5 inches and standard deviation
approximately equal mean and 2.6. If 40 students had neck circumference of 19.7 or
standard deviations? higher, how many students had neck circumference of
(A) {5, 5, 5, 5, 5} 11.9 or lower?
(B) {3, 1, 2, -1, 5} (A) 20
(C) {4, -10, 2, 3, 1} (B) 40
(D) {2.1, 3.1, 4.1, 5.1, 6.1}
(C) 140
(E) {25, 35, 45, 55, 65}
(D) 160
(E) 320
2. The earnings of 100 workers in a certain
company are normally distributed. If
the mean is 24 and standard deviation
is 4, then find an approximate value for
the range.
(A) 4.5
(B) 8
(C) 24
(D) 36
(E) 48

3. A set consist of 96 elements. The range

of the set is 10 and mean is 12.6

Column A Column B
SD of the set 10

4. The score of 2 golfers for 24 rounds follows normal

distribution with range 2.4 and mean 72. Find standard
deviation?
(A) .25
(B) .4
(C) .8
(D) 1.2
(E) 2.3

Page # 214
 Descriptive Statistics - Percentiles and Quartiles

Percentile

The pth percentile is a value such that at least p percent of the data are less than or equal to this value and at least
(100-p) percent of the data are greater than or equal to this value.

Calculating the pth percentile:

1. Order data from smallest value to highest value.

2. Calculate index i : i = (p/100)n where p is the percentile in question and n is the number of data.
3. If i is not an integer, the next integer greater than i is the position of the pth percentile.
4. If i is an integer, the pth percentile is the average of the value in position i and i+1.

Quartiles

Quartiles divide the whole series into 4 equal parts. So there are 3 quartiles namely first Quartile denoted by Q1, second
Quartile denoted by Q2 and third Quartile denoted by Q3. Second Quartile is nothing but Median. Since it denotes the
position of the item in the series, it is a positional average.

NOTE: Whenever we find quartiles, we have to arrange the data in the ascending order.

Upper Quartiles-Lower Quartiles-InterQuartile Range

Upper quartile is nothing but the third quartile. The upper quartile (Q3) is the median of the upper half of the data set.
Whereas the lower quartile is nothing but the first quartile. The second quartile is also known as median. Interquartile
range is 9  9#

Page # 215
 QUESTIONS:

1. Find the first quartile of the following data: 3, 5, 6, 7, 9, 22, 33.

2. Find the 85th percentile of students’ weight: 110, 125, 126, 113, 105, 123, 130, 122, 122, 110, 115, 118.

3. Find the Third Quartile of the following marks:-

21, 12, 36, 15, 25, 34, 25, 34

4. Use the following data to answer the questions below:

79, 53, 82, 91, 87, 98, 80, 93, 86

a) What number represents the 50th percentile of the data?

b) What number represents the 25th percentile of the data?

c) What number represents the 75th percentile of the data?

5. Find the inter quartile range of the following numbers.

12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25

6. Determine the 30th percentile of the following nine numbers 1 2 4 3 5 3 5 2 6

Page # 216
Measures of Dispersion

Measures of dispersion indicate the degree of “spread” of the data. The most common statistics used as
measures of dispersion are the range, the interquartile range, and the standard deviation. These statistics
measure the spread of the data in different ways.

The range of the values in a group of data is the difference between the greatest number G in the data and the
least number L in the data; that is, G-L. For example, the range of the five numbers 11, 10, 5, 13, 21 is
21  5 16

The simplicity of the range is useful in that it reflects the maximum spread of the data. However, sometimes a
data value is so unusually small or so unusually large in comparison with the rest of the data that it is viewed
with suspicion when the data are analyzed; the value could be erroneous or accidental in nature. Such data are
called outliers because they lie so far out that in most cases, they are ignored when analyzing the data.
Unfortunately, the range is directly affected by outliers.

A measure of dispersion that is not affected by outliers is the interquartile range. It is defined as the difference
between the third quartile and the first quartile, that is, 9  9# Thus, the interquartile range measures the

spread of the middle half of the data.

One way to summarize a group of numerical data and to illustrate its center and spread is to use the five
numbers ;, 9# , 9 , 9 < =.

These five numbers can be plotted along a number line to show where the four quartile groups lie. Such
plots are called boxplots or box and whisker plots, because a box is used to identify each of the two middle
quartile groups of data, and “whiskers” extend outward from the boxes to the least and greatest values.

Page # 217
 Example 1 : In the list of 16 numbers 2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, the range is 9  2
7, the
first quartile, is 9# = 6, and the third quartile is 9 8.5. So the interquartile range for the numbers in this
list is 8.5 – 6 = 2.5

A boxplot for this list of 16 numbers is shown in Data Analysis Figure below. The boxplot is plotted over a
number line that goes from 0 to 10.

From the boxplot, you can see that for the list of 16 numbers, the least value L is 2, the first quartile9# is
9 is 8.5, and the greatest value G is 9. In the boxplot, the box
6, the median M is 7, the third quartile
extends from 9# @A9 with a vertical line segment at M, breaking the box into two parts; that is to say,

9# @A ; that is from 6 to
from 6 to 8.5, with a vertical line segment at 7. Also, the left whisker extends from

9 @A = that is from 8.5 to 9.

2; and the right whisker extends from

There are a few variations in the way boxplots are drawn—the position of the ends of the boxes can vary
slightly, and some boxplots identify outliers with certain symbols—but all boxplots show the center of the
data at the median and illustrate the spread of the data in each of the four quartile groups. As such,
boxplots are useful for comparing sets of data side by side.

Page # 218
 Example 2 : Two large lists of numerical data, list I and list II, are summarized by the box plots in Data
Analysis Figure 11 below.

The above two box plots are plotted over a number line that goes from 100 to 900, with equally spaced
tick marks representing multiples of 100.

In the boxplot for list I, the left whisker extends from 200 to 270; the box extends from 270 to 700; a
vertical line segment at 450 breaks the box into 2 parts; and the right whisker extends from 700 to 720.

In the boxplot for list II, the left whisker of the boxplot extends from 250 to 380; the box extends from 380
to 600; a vertical line segment at 550 breaks the box into 2 parts; and the right whisker extends from 600 to
750.

Note that all of the numbers read from the boxplot are approximate.

Based on the boxplots, several different comparisons of the two lists can be made. First, the median of list II,
which is approximately 550, is greater than the median of list I, which is approximately 450. Second, the two
measures of spread, range and interquartile range, are greater for list I than for list II. For list I, these measures
are approximately 520 and 430, respectively; and for list II, they are approximately 500 and 220, respectively.

Page # 219
DIFFERENT WAYS OF COUNTING ­
(PERMUTATION & COMBINATION)

1. Each night before he goes to bed, 4. Kris is purchasing gear to ride his bike
Jordan likes to pick out an outfit to this winter. He wants to buy 2 pairs of
wear the next day. He has 12 different gloves, 1 parka, 2 hats and 3 pairs of
shirts, 10 different pairs of jeans and 8 boots. If the catalog from which he will
pairs of sneakers. If an outfit consists of order offers 5 types of gloves, 3
1 shirt, 1 pair of jeans, and 1 pair of different parkas, 4 hats, and 6 pairs of
sneakers, how many different outfits boots, how many different orders could
does Jordan have? he place?
(A) 30 (A) 360
(B) 90 (B) 720
(C) 240 (C) 3600
(D) 480 (D) 7200
(E) 960 (E) 36000

2. Five people are running in a race. The 5. Greg is rent movies from the video
first one to finish wins a gold medal, the store. He must choose 3 videos from a list
second one wins a silver medal and the of 10 videos and decide in which order to
third wins a bronze medal. How many watch them. How many
different arrangements of medal different schedules of videos can he
winners, in order from first to third are create?
possible? (A) 30
(A) 5 (B) 70
(B) 10 (C) 700
(C) 60
(D) 720
(D) 120 (E) 1000
(E) 125

6. Doug is selecting books to read on his

3. Five people are running in a race. The vacation. He must choose 1 poetry
first three to finish win gift certificates. book, 1 novel, 1 self-help book, and 1
How many different groups of people pop-up b story book from his collection. If
could win the gift certificates? his collection includes 5 poetry books, 3
(A) 5 novels, 4 self help book, and 10 pop- up
(B) 10 story books, how many different
(C) 60 selections are possible?
(D) 120 (A) 22
(E) 125 (B) 128
(C) 500
(D) 600
(E) 1040

Page # 220
7. Carol is buying birth day gifts for her 10. In how many ways can 4 ladies and 5
niece. She has a list of 10 potential gifts gentlemen be seated in a row so that no
to choose from, but she can only afford two ladies sit together?
to buy 2 gifts. How many different pairs of (A) 43200
gifts can Carol buy? (B) 21600
(A) 10 (C) 5760
(B) 20 (D) 2880
(C) 45 (E) 1440
(D) 90
(E) 200 11. Right triangle PQR is to be constructed
in the xy -plane so that the right angle is
at P and PR is parallel to the x-axis. The
x and y coordinates of P, Q, and R are to
8. Ben needs to form a committee of 3 be integers that satisfy the inequalities
from a group of 8 engineers to study - 5 ≤x ≤ 4 and 7 ≤ y ≤ 17. How many
design improvements for a product. If different triangles with these properties
two of the engineers are too could be constructed?
inexperienced to server together on the (A) 110
committee, how many different (B) 1,100
committees can Ben form? (C) 9,900
(A) 20
(D) 10,000
(B) 30
(E) 12,100
(C) 50
(D) 56 12. How many diagonals are there in an
(E) 336 octagon?
(A) 56
(B) 28
(C) 20
9. Jack receives instructions from 12
clients and uses color coding to identify (D) 16
each client. If either a single color or a (E) 8
pair of two different colors is chosen to
represent each client and if each client 13. Alex intends to go from corner M to
is uniquely represented by that choice corner N of the garden which has
of one or two colors, what is the pathways as shown in the figure.
minimum number of colors needed for
the coding? (Assume that the order of
the colors in a pair does not matter.)
How many routes can Alex take
(A) 4
ensuring that he travels the minimum
(B) 5
possible distance?
(C) 6
(D) 12 (A) 6
(E) 24 (B) 8
(C) 10
(D) 14
(E) 16
Page # 221
14. How many parallelograms are formed when a 18. (i) How many arrangements are possible using the letters
set of five parallel lines intersect another set of four of the word BAHAMA?
parallel lines? (A) 36
(A) 120 (B) 50
(B) 60 (C) 81
(C) 36 (D) 120
(D) 20 (E) 720
(E) 10
(ii) How many words can be formed
15. In how many ways can 3 Canadians, such that they have H and M
2 Americans and an Indian be arranged in a together?
row so that the 3 Canadians are always
(A) 20
together and the two Americans are
always together? (B) 40
(A) 360 (C) 60
(B) 216 (D) 108
(C) 72 (E) 120
(D) 60 (iii) How many words can be formed
(E) 36 such that they begin with H and end
with M?
16. There are 5 students and 3 teachers. In
how many ways can a team of 5 be formed (A) 24
so that there is at least one teacher but not
(B) 12
more than two teachers in the team?
(A) 450 (C) 8
(B) 180 (D) 6
(C) 60 (E) 4
(D) 45 (iv) How many words can be formed
(E) 30 such that all vowels are together?

(A) 24
(B) 12
17. There are 4 letters A, B, C and D that have (C) 8
to go into 4 envelopes addressed to a, b, c
(D) 6
& d respectively. In how many ways can the
4 letters be put in the 4 envelops such that (E) 4
every letter goes into a wrong envelope?
(A) 20
(B) 12
(C) 9
(D) 6
(E) 4

Page # 222
(v) How many words can be formed
such that they begin with H and end with A?

(A) 24
(B) 12
(C) 8
(D) 6
(E) 4

Page # 223
 PROBABILITY 4. Kevin flips a coin four times. What is the
probability that he gets heads on at least
one of the four flips?
1. Stephen own 20 Arrow shirts: 6 of them are (A) 1/16
long-sleeved, 11 of them are short sleeved, and 3 of (B) 1/4
them are sleeveless. If he chooses a shirt at random, (C) 3/4
what is the probability that the shirt will not be (D) 13/16
short-sleeved? Type your answer in the boxes (E) 15/16
provided.
5. A bag of candies has 12 red, 5 green, and 13 orange colored
candies. If a candy is chosen from the bag at random, what
it the probability that the candy will not be green?
(A) 5/6
(B) 3/5
(C) 13/20
2. A six-sided die with faces numbered one through six is
rolled twice. What is the probability that the face with (D) 2/5
the number 2 on it will not be facing upward on either (E) 1/6
roll?
(A) 1/6
(B) 2/3
6. If a value for x is chosen at random from set A = {-8, -1, 0, 3,
(C) 25/36
4, 12}, what is the probability of choosing an even value for
(D) 17/18 x?
(E) 35/36 (A) 0
(B) 1/6
3. If x is to be chosen at random from the set (1, 2, 3, 4) (C) 2/3
and y is to be chosen at random from the set (5, 6, 7)
(D) 1/2
what is the probability that xy will be even?
(A) 1/6 (E) 5/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6

Page # 224
7. A candy dish contains 6 oranges and 4 lime gumdrops. 10. There are 5 red balls and 6 black balls in a bowl. Two balls
If two gumdrops are drawn from the dish at a time, are picked up at random simultaneously. What is the
what is the probability that both gumdrops will be probability of the two balls being of the same color?
orange? (A) 10/11
(A) 2/15 (B) 6/11
(B) 1/3 (C) 5/11
(C) 9/25 (D) 2/11
(D) 3/5 (E) 1/11
(E) 2/3
11. There are three red balls and some black
and some green balls in a bowl. If the
8. There are 100 cards numbered from 1 probability of randomly picked up ball being
to 100. If three cards are selected at red is 1/5. How many non red balls are here
random and with replacement, what is in the bowl?
the probability that the sum of the three (A) 12
numbers on the cards so selected will be (B) 10
odd? (C) 9
(A) 1/4
(D) 6
(B) 3/8
(E) 3
(C) 1/2
(D) 5/8 12. A two-sided coin (not the ‘Sholay’ coin) is
(E) 3/4 tossed three times. What is the probability
that ‘heads’ will be the result exactly
9 . A die with x sides has consecutive integers on its sides. twice?
If the probability of not getting a 4 on either of the two (A) 3/4
tosses is 36/49, how many sides does the die have? (B) 2/3
(A) 4 (C) 1/2
(B) 5 (D) 3/5
(C) 7 (E) 3/8
(D) 8
(E) 13 13. A certain box contains only black, blue and
red pens. If the probability of choosing a
black pen is 1/4 and the probability of
choosing a blue pen is 1/6. What is the
probability of choosing a red pen?
(A) 1/24
(B) 1/12
(C) 7/12
(D) 3/4
(E) Answer cannot be determined

Page # 225
14. Probability of raining on any day in a certain week is 18. Two dices are thrown together. What is
50%. What is the probability that it rains exactly 3 days in the probability of getting a total of at
a span of 5 days? least 6?
(A) 1/32 (A) 1/3
(B) 1/16 (B) 1/2
(C) 1/8 (C) 2/3
(D) 5/16 (D) 13/18
(E) 3/8 (E) 8/9

15. Probability of A attending class is 1/6,

probability of B attending class is 1/5.
What is the probability that either A alone 19. In a group of 8 persons what is the
or B alone attends class? probability that at least two of them are
(A) 1/10 born on the same day of the week?
(B) 1/5 (A) 1/8
(C) 3/10 (B) 1/7
(D) 1/3 (C) 1/4
(E) 11/30 (D) 1/2
(E) 1
16. A single die with six faces numbered 1
though 6 is thrown twice. If the numeral
that faces upward as the result of each 20. In a defective six-sided dice the probability of getting an odd
throw is recorded, what is the probability number is twice the probability of getting an even number.
that the sum of two numbers is less than What is the probability of getting 5 in a single throw?
10? (A) 1/18
(A) 5/6 (B) 1/9
(B) 2/3 (C) 2/9
(C) 1/2 (D) 1/2
(D) 1/3 (E) 2/3
(E) 1/6

17. In a drawer of shirts, 8 are blue, 6 are

green and 4 are magenta. If Mason draws
2 shirts at random, what is the probability
that at least one of the shirts he draws
will be blue?
(A) 25/153
(B) 23/153
(C) 5/17
(D) 4/9
(E) 12/17

Page # 226
21. If three letters are put in three envelops
with three different addresses, what is
the probability that no addressee
receives the correct letter?
(A) 1/6
(B) 1/4
(C) 1/3
(D) 1/2
(E) 2/3

22. A junior class has 1000 students and a

certain senior class 800 students.
Among these students there are 60
sibling pairs, each consisting of one
junior and one senior. If 1 student is to be
selected at random from each class, what is
the probability that the 2
students selected will be a sibling pair?
(A) 3/40,000
(B) 1/36000
(C) 9/2000
(D) 1/60
(E) 1/15

Page # 227
MISCELLANEOUS
5. x is a positive integer.
1. If the nth term of a sequence is given by
the expression 2 * 4n-1, what is the value of
Column A Column B
the unit’s digit of the 131st term in
the sequence?
Number of Number of
(A) 0
distinct prime distinct prime
(B) 2
factors of x factors of x 3
(C) 3
(D) 6
6. Regular Polygons P and Q have equal
(E) 8 perimeters. Polygon P has n sides;
Polygon Q has (n+1) sides.
Column A Column B
2. For all real numbers r, the operation r * Area of Polygon P Area of Polygon Q
is defined by the equation r * = r - r/4.
If (r*)* = 9, then r =
(A) 12
7. x is an integer such that 2 x is a factor of
(B) 16
12!
(C) 20 Column A Column B
(D) 24
(E) 28 The greatest possible value for x 9

3. For all non-negative real numbers p, q 8. z is the least even integer greater than - 1.

and r, let be defined by the

Column A Column B
equation = B*C  ). (x is a non-
negative real number) The value of xyz 0

Column A Column B
9. If n is the least integer greater than 5.3,
then n! must be divisible by which of the
following numbers?
(A) 7
(B) 11
4. For all x and y, define φ xy as follows (C) 12
(D) 13
φ xy = - x − y
(E) 14
Column A Column B

φ 2(-3) -5

Page # 228
10. x and n are positive integers, such that If a, b, c, d, e, f and g are distinct
n > x. integers, which of the following must be
true?
Column A Column B (A) Range P ≥ Range Q
(B) Mean P = Mean Q
The remainder (C) Range P ≠ Range Q
when n! + x is 0 (D) Median P ≠ Median Q
divided by x (E) Range P > Range Q

14. x = Number of ways 25 marbles can be

placed in 6 bowls, such that at least one
11. At Rocktown College, the 400 students bowl has 5 or more marbles
taking Psychology received an
y = Number of ways 25 marbles can be
average score of 76 on the final exam
placed in 6 bowls
and the scores had a normal
distribution. The bottom 16 percent of Column A Column B
the scorers will receive a failing grade
and 8 students received a score of 96 or x y
higher.
15.

Column A Column B

Score at or below
which the
students fail the 56
course
Column A Column B

Area of the circle 36 π

12. If the range of the set of numbers {150,
16. 11a > 13
90, 125, 110, 170, 155, x, 100, 140} is
95, which of the following could be x?
Column A Column B
(A) 80
(B) 85
a2 a
(C) 95
(D) 125 17.
(E) 185 (i) if ab > b

(ii) if 5a > 7b

13. Set P = {a, b, c, d, e, f, g} & Column A Column B

Set Q = {a, b, c, d, e, f}
a b

Page # 229
 SELECT ONE OR MORE ANSWERS PRACTICE

Page # 230
 4.a)

NUMERIC ENTRY PRACTICE

4. b)

Page # 231
 5.

(a)

(b)

6.

(a)

(b)

Page # 232
MATH ANSWER KEYS
Trap Ans, BP & POE Plugging In Drill Geometry Charts
Qn # Answer Qn # Answer Qn # Answer Qn # Answer
1 C 1 D 1 E 1 B,F
2 C 2 C 2 E 2 D
3 D 3 E 3 D 3 C
4 D 4 E 4 B 4 B
5 C 5 E 5 A 5 A
6 B 6 B 6 A 6 B
7 D 7 D 7 B 7 D
8 B 8 C 8 B 8 C
9 D 9 E 9 D 9 A
10 D 10 D 10 E 10 B
11 E 11 C 11 28.9
12 B 12 D 12 48
13 A,D 13 C 13 D
14 B,C 14 B,D 14 D
15 D 15 6 15 E
16 A 16 C 16 C
Fundamentals 17 A 17 D 17 E
Qn # Answer 18 E 18 D 18 E
1 D 19 B 19 D 19 B
2 11 20 D 20 65 20 B
3 C 21 B 21 C 21 D
4 B 22 C 22 A 22 C
5 B 23 C 23 E 23 E
6 D 24 C 24 A 24 15
7 D 25 D 25 C 25 66
8 E 26 E 26 C 26 B
9 A 27 E 27 A 27 C
10 C 28 D 28 D 28 A
11 C 29 B 29 D 29 C
12 C 30 C 30 E 30 B
13 C 31 C 31 B
14 D 32 C 32 D
15 D 33 D 33 D
16 D 34 D 34 4
17 D 35 C 35 A
18 D 36 A 36 D
19 C 37 C
20 A 38 B
21 B 39 B
22 A,B,C 40 C
23 C 41 A
24 A,B,D 42 D
25 C 43 D
26 D 44 D
27 B
28 A
29 60
30 C

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Co‐ordinate Geometry Std Deviation 5 A
Qn # Answer Qn # Answer 6 C
1 D 1 B 7 B
2 A 2 C 8 C
3 E 3 B 9 C
4 B 4 B 10 C
5 D 5 E 11 A
6 B 12 E
7 D Quartiles 13 C
8 A 1) 5 4a) 86 5) 24 14 D
9 E 2) 126 4b) 79.5 6) 2 15 C
10 B 3) 34 4c) 92 16 A
11 C Perm & Comb 17 E
12 E Qn # Answer 18 D
13 A 1 E 19 E
14 C 2 C 20 C
15 C 3 B 21 C
16 B 4 C 22 A
17 B 5 D
18 B 6 D
19 D 7 C
20 D 8 C
Arithmetic Progression 9 B
Qn # Answer 10 A
1 C 11 C Miscellaneous
2 B 12 C Qn # Answer
3 B 13 C 1 B
4 D 14 B 2 B
5 A 15 C 3 D
6 B 16 D 4 C
17 C 5 C
S.I. & C.I. 18a D 6 B
Qn # Answer 18b B 7 A
1 B 18c E 8 C
2 B 18d A 9 C
3 C 18e B 10 C
4 B 11 A
5 B Probability 12 E
6 B Qn # Answer 13 A
7 A 1 9/20 14 C
8 B 2 C 15 A
9 A 3 D 16 A
4 E 17 D and A
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 Select one or more choices

1. A, B
2. A, B, D
3. B, C, D, E

4. a) C

NUMERIC ENTRY PRACTICE

4. b) 108.7

5. (a) Range = 41, 9# 114, 9 118, 9 126, D@E)CF)@GHE )IE 12

(b) 40

6. (a) 1440
(b) 0.15

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