Mathematical

Reasoning
1. Chart 1 gives the year on year growth in % of various sectors in 1996-97. Chart 2 givesthe weight of
each of these sectors in the overall industrial output of the country for the 1995-96. Wherever the weights
in the year 1996-97 are needed, if nothing is specified, take it same for the year 1996-97 also

What was the % YOY growth in industrial output, between the two years?

A 4.89%

B 9.52%

C 7.9%

D 10.1%
Ans: 9.52%

Percentage YOY growth in industrial output

= (15 x 0.22) + (10 x 0.06) + (9 x 0.07) + (13 x 0.22) + (2 x 0.17) + (4 x 0.04) + (13 x 0.10) + (3 x 0.11)
= 9.52 %

2. Which group of shapes can be assembled to make the shape shown?

Ans: C

Just observe the images in the options and you will see the three shapes in the third option make up the
image

3. Which pattern makes up the cube shown below?

Ans: A

Just look at the nets carefully and imagine how it folds up into the above cube.

4.

Note: Figure NOT drawn to scale.

AB=BC

CD=BC+6

DE=1/2(CD)

Give AE in terms of DE.

A AE=6(DE)+6

B AE=6(DE)−6

C AE=7(DE)+6

D AE=7(DE)−12

Ans: D

Since DE=1/2(CD), CD=2(DE)

Since CD=BC+6, BC=CD−6=2⋅DE−6, and, subsequently, AB=2(DE)−6

 

AE=AB+BC+CD+DE

=[2(DE)−6]+[2(DE)−6]+2(DE)+DE

=2(DE)+2(DE)+2(DE)+1(DE)−6−6

=7(DE)−12

5. Choose the correct option in place of question mark (?) in the following series:

21, 25, 33, 49, 81, (?).

A 145

B 122

C 195

D 119

Ans: 145

25 – 21 = 4 = 2^2

33 – 25 = 8 = 2^3

49 – 33 = 16 = 2^4

81 – 49 = 32 = 2^5

Now,

21 + 2^2 = 21 + 4 = 25

25 + 2^3 = 25 + 8 = 33

33 + 2^4 = 33 + 16 = 49

49 + 2^5 = 49 + 32 = 81

81 + 2^6 = 81 + 64 = 145

6. C= 5/9(F-32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a
temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree

Celsius.

A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees

Fahrenheit.

A temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree

Celsius.

A I only
B II only
C III only
D I and II only

Ans: D

Think of the equation as an equation for a line

y=mx+b

where in this case C=5/9(F-32)

Here the slope is 5/9 which means a 1 degree rise in Fahrenheit is 5/9 degree of degree celcius.

So, celcius is 9/5 rise per Fahrenheit which is 1.8 degree.

So, statement 1 and 2 are true.

7. The equation 

(24x2+25x−47)/ax-2 = −8x−3−(53/ax-2)

 is true for all values of x≠2/a, where a is a constant.

What is the value of a?

A -16
B -3
C 3
D 16

Ans: B
There are two ways to solve this question. The faster way is to multiply each side of the given equation
by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

The other option which is longer and more tedious is to attempt to plug in all of the answer choices for a
and see which answer choice makes both sides of the equation equal. Again, this is the longer option, and
I do not recommend it for the actual SAT as it will waste too much time.

8. If x <6, find x

|x - 7| - 4|-6|=5

A 10

B -11

C -22

D 7

Ans: -22

If x is lesser than 6 then |x - 7| becomes –(x-7) and |-6| becomes 6

Solving,

-(x-7)-24=5

X=-22

9. If an image is mirrored and then scaled 2.5 times its own size and then is rotated by 180 degrees on the
XY then what is the angle difference between the initial image and the final image on the YZ plane?

A 0 degrees
B 30 degrees

C 90 degrees

D 180 degrees

Ans: 180 degrees

The reflected image is always rotated by180degrees

10. Arpit, Bimal, Chatur, Dinu and Elan has participated in a tournament namely ‘Freaket’ and played 4
matches in total. The below table gives partial information about their individual scores and total runs
scored by them in each match as a team.

In the following table, each column has 2 values missing. The missing scores are scored by 2 lowest
scorers in that match. None of the two missing values is more than 10% of the total runs scored in that
match.

What is the maximum percentage% contribution done by Arpit in the four matches?

A 19.7%       

B 19.9%

C 20.1%

D 20.2 %
Maximum possible runs scored by Arpit in Match-1 = 27

Maximum possible runs scored by Arpit in Match-3 = 19

Maximum possible percentage contribution:

(27+100+19+53)/(270+300+240+200)x100%=199/1010x100%= 19.7%

11. Which of the cubes shown could be made from the pattern?

Ans: A

The key to these questions is to remember that only three faces of the cube can be shown in the
illustration, this means that you need only consider the relationship between the three visible elements on
each cube and see if the same relationship exists in the pattern.
11.

A person is on Day street and can see the townhall to her right, What direction is she facing?The person
turns right and then turns left on the main street and then takes the next right. Which point is the person
closest to?

A South, O

B North, N

C South, M

D East, M

Ans: South, M

Just follow the directions and use the map to end up with option C
12. How many blocks are there in the image if there are x/13 hidden blocks behind, where x is the number
of visible blocks.

Ans: A

By looking at the image we see there are 26 blocks

So, hidden blocks are 26/13=2 blocks

So, total blocks are26+2=28 blocks

13. Big Bob the, 8-feet tall warehouse foreman is stacking uniformly sized boxes of goods in the
warehouse. Big Bob notices that he is the exact same height as 3 boxes stacked on top of each other. If the
warehouse ceiling is 55 feet high, what is the maximum number of boxes that he can stack on top of one
another before he hits the ceiling?

A 14

B 23

C 20
D 34

Ans: 20

To find the height of each box set the 3 boxes equal to the height of Big Bob. So, let x be the height of
each box. Then,

3x=8 feet or x=8 feet/3=2.66 feet

Therefore to find the maximum number of boxes that fit under the ceiling, we divide the ceiling height by
the height of each box. So,

55′/2.66′=20.68 or 20 whole boxes would fit under the ceiling.

14. What is the missing letter in the series?

A Q

B V

C W

D Y

Ans: V

Write the sequence separately and observe the letter closely. You will notice that the letters are not in
order. There are missing letters in between. Write those missing letters.
P   Q   R   S   T  __    X

Now if you observe the letters, it is very clear that the consecutive letters are missing if we go by the
universal sequence of 26 letters of English Alphabets. And the letter next to the consecutive letter is part
of the sequence. So in the sequence of English Alphabets ‘U’ is the consecutive letter of ‘T’ or ‘U’ comes
next to ‘T '.So we will drop ‘U’. And the letter next to ‘U’ ie ‘V’ will become part of the series or
sequence.

15. If 4x-y=13 then what is the value of 16x/2y?

A 2

B 213
C 22

D 24

Ans : 213

Write the fraction as 24x/2y

It becomes 2(4x-y)

Using equation we get the value as 213

16. Let f(x) = x2 + 13x + 1. Which of the following statements is NOT true?
A. f(x) has a maximum value
B. The graph of f is not a line
C. The graph of f has no x-intercepts.
D. The graph of f has a y-intercept.

Ans: A

Only A is false as the maximum value cannot be attained as we don’t have roots for the equation

17. Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.

The total amount of bonus paid by the company during the given period is approximately what percent of
the total amount of salary paid during this period?
A 0.5%

B 1%

C 2.5%

D 0.25%

Ans: 1%

Percentage=[(3+2.52+3.84+3.68+3.96)/(288+342+324+336+420)]x100%=[17/1710]x100%=1%(approx)

18. Identify the correct 2D representation.

Ans: A

Just imagine the top view and you will find option A correct
19. Which of the boxes comes next in the sequence?

Ans: B

Squares are in no particular order within the frame. It is merely the number of squares that are important
for this sequence. Shaded squares change from three to two with each turn. Unshaded squares change
from two to three with each turn. Semi-circle moves from top left to top right, to bottom left to bottom
right with each turn.

20. Restate 200 feet per second in miles per hour (nearest whole number).

A 78 mi/hr

B 136 mi/hr

C 49 mi/hr

D 143 mi/hr

Ans: 136 mi/hr

1 mile is 5280 feetand 1 hour is 3600 seconds

Conversion is as follows

200ft/1 sec= 200x3600/1x5280=136 4/11 miles per hour

Round of to 136 miles per hour

21. Find the pattern in the given series and find the number in place of ‘?’
4, 11, 19, 41, ?, 161
A 62
B 108
C 79
D 90

Ans: 108

4 × 2 + 3 = 11
11 × 2 – 3 = 19
19 × 2 + 3 = 41
41 × 2 – 3 = 79
79 × 2 + 3 = 161

22.

A 4

B 7

C 5

D 8

Ans: 5
23. The 30 members of a club decided to play a badminton singles tournament. Every time a member
loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that
must be played to determine the winner ?

A 30

B 15

C 29

D 40

Ans: 29

The minimum number of matches if no matches are repeated and there are no ties then (n-1) matches
which is 30-1=29 matches

24. Points A and B lie on a circle with radius 1, and arc AB has a length of π /3. What fraction of the
circumference of the circle is the length of arc AB?

A 0.235

B 0.114

C 1.117

D 0.167

To figure out the answer to this question, you'll first need to know the formula for finding the
circumference of a circle.

The circumference, C, of a circle is C=2πr, where r is the radius of the circle. For the given circle with a
radius of 1, the circumference is C=2(π)(1), or C=2π.

To find what fraction of the circumference the length of AB  is, divide the length of the arc by the
circumference, which gives π /3÷2π. This division can be represented by 

π/3 x 1/2 π = 1/6

The fraction 1/6 can also be rewritten as 0.166 or 0.167.

 25.

A 50,77

B 50,98

C 33,77

D 45,68

Ans: 50, 77

26. A is 3 years older to B and 3 years younger to C, while B and D are twins. How many years older is C
to D?

A 3

B 5

C 7

D 6

Ans: 6

If A is 3 yrs older than B and 3 yrs younger than C then C is 6 yrs older than B. B and D are of same age
so C is 6 years older than D.
27.Identify the pattern.

A 34

B 81

C 100

D 113

Ans: 100

The pattern is

AB=(A+B)^2

So  (1+9)^2=10^2=100

28. Study the bar chart and answer the question based on it.
The average production of 1996 and 1997 was exactly equal to the average production of which of the
following pairs of years?

A 2001 to 2003

B 2000 to 2007

C 1995 to 2001

D 1999 to 2000

Ans: 1995 to 2001

Average production of 1996 and 1997 40+60/2=50

2000 and 2001 50 + 75

= 62.5.
=
2

1999 and 2000 65 + 50

= 57.5.
=
2

1998 and 2000 45 + 50

= 47.5.
=
2

1995 and 1999 25 + 65

= 45.
=
2

1995 and 2001 25 + 75

= 50.
=
2

The average production of 1996 and 1997 is equal to the average production of 1995 and 2001.

29. 8-i/3-2i
If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value
of a? (Note: i=√−1)

A 1

B 2

C 3

D 4

Ans: 2

To rewrite 8-i/3-2i in the standard form a+bi, you need to multiply the numerator and denominator of 8-
i/3-2i by the conjugate, 3+2i. This equals

24+16i-3+(-i)(2i)/32-2i2

Since i2=−1, this last fraction can be reduced simplified to

26+13i/13

which simplifies further to 2+i. Therefore, when 8-i/3-2i is rewritten in the standard form a + bi, the value
of a is 2.

30.

A 69

B 79

C 89

D 99

Ans: 79