# Common Quantitative Comparison Practice Test 1

Question – 1

1. Area of a right triangle is 504 sq.cm. The length of the hypotenuse is 65 cm.?

Column-A Column-B
Sum of the sides containing the right angle Length of the hypotenuse

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

The sum of any two sides of a triangle is always greater than the third side. Hence, option A is correct.

Question – 2

2. Consider the sequence -9, -5, -1, 3,….?

Column-A Column-B
The 50th term 191

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Let the first term of the sequence be a and the common difference be d.
a= -9
d = -1-(-5) = 5-1=4
The nth term of the sequence is given byTn=a+(n-1)d
=-9+(50-1)4
=-9+49*4
=-9+196
=187
The 50th term is 187
Option B is correct

Question – 3

3.

Column-A Column-B
Number of ways in which one person can be selected from a group of 10 Number of ways in which two persons can be chosen from a group of 20

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

One person can be selected from a group of 10 in C(10,1) ways
C(10,1)=10!/[1!9!] =10
Two persons can be selected from a group of 20 in C(20,2) ways
C(20,2)=20!/[2!18!]
=20*19/2=10*19=190
Option B is correct.

Question – 4

4. logx/2=logy/3=logz/5.?

Column-A Column-B
xy yz

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Let logx/2=logy/3=logz/5=k
logx=2k, logy=3k and logz=5k
logx+logy = 2k+3k=5k
log(xy) = 5klogy+logz = 3k+5k=8k
log(yz) = 8k

log(xy)

Question – 5

5. The average of the marks obtained by 30 students of a class is 50. If the score of one student is removed, the average reduces by 1.?

Column-A Column-B
Average score of the remaining students The score that was removed

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Average = Total marks/number of students
Total marks = Average*number of students
= 50*30 = 1500New average = 50-1=49
Number of students = 30-1=29
Total marks = 49*29
= 1421
Marks of the student = 1500-1421
= 79
The score that was removed = 79
Average score of the remaining students = 49
Option B is correct.

Question – 6

6. A square is constructed taking a side of a rectangle as a side of the square.?

Column-A Column-B
Perimeter of the square Perimeter of the rectangle

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

We do not know whether the square is along the length or along the breath of the rectangle.
Hence, we cannot compare the perimeters.
Option D is correct.

Question – 7

7. A point divides the line joining (-1,-5) and (6,5) in the ratio 1:6.?

Column-A Column-B
Ordinate of the point Abscissa of the point

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

The coordinates of the point are given by
((-1*6+6*1)/(6+1), (-5*6+5*1)/(6+1))
= ((-6+6)/7, (-30+5)/7)
= (0, -25/7)
Abscissa is the x co-ordinate and hence it is greater than the ordinate, which is the y co-ordinate.
Option B is correct.

Question – 8

8.

Column-A Column-B
Number of two-digit numbers Number of three-digit numbers less than 250

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Number of two-digit numbers = 99-9=90
Number of three-digit numbers less than 250=250-99=151
90<151
Option B is correct.

Question – 9

9.

Column-A Column-B
Number of vertices of a rectangle Number of triangles that can be formed from the vertices of a rectangle

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Number of vertices of a rectangle = 4
Number of triangles that can be formed from the vertices of a rectangle = C(4,3)
= 4!/(3!1!)
= 4
Hence, option C is correct.

Question – 10

10.

Column-A Column-B
Perimeter of a square with each side 29 cm long. Perimeter of a rhombus whose diagonals are 40cm and 42cm long

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Perimeter of the square = 29*4=116 cm
The diagonals of a rhombus bisect each other at right angles.
Thus, the rhombus is divided into 4 congruent right triangles.
The hypotenuse of any triangle is a side of the rhombus.
Applying Pythagoras theorem, we get
Hypotenuse = Sqrt[(40/2)^2+(42/2)^2]
= sqrt(20^2+21^2)
= sqrt(400+441)
= sqrt(841)
= 29cm
Perimeter of the rhombus = 4*29
= 116 cmOption C is correct.
[20^2=20*20]

Question – 11

11. The radius of a circle is 49cm. Each side of a square is equal to the diameter of the circle.?

Column-A Column-B
Area of the square Area of the circle

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Area of the circle = pi*r^2, where r is the radius of the circle
Area = 22/7*49*49=7546 sq.cm.Each side of the square = 2*radius
= 2*49 = 98cm
Area of square = side*side
= 98*98
=9604 sq.cm.

Option A is correct.
[pi=22/7, r^2=r*r]

Question – 12

12. A chord of length 112 cm is at a distance of 33 cm from the centre. ?

Column-A Column-B
Length of the chord. Radius of the circle

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

A line drawn from the center of the circle perpendicular to the chord will bisect the chord.
This line, the radius of the circle and the chord form a right triangle.
Applying the Pythagoras theorem to the triangle, we get
Hypotenuse = sqrt[base^2+perpendicular^2]
= sqrt[(112/2)^2+33^2]
= sqrt[56^2+1089]
= sqrt[3136+1089]
= sqrt(4225) = 65cm
Radius of the circle is 65 cm.
Length of the chord is 112 cm.
Option A is correct.
[x^2=x*x]

Question – 13

13. The population of a town is 140000. It increases by 5% in the first year. In the second year, it decreases by 10%.?

Column-A Column-B
Population after the first year Population after the second year

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

This problem is similar to a problem of compound interest.
Population after 1 year = 140000(1+5/100) = 147000
Population after 2 years = 147000(1-10/100) = 132300
Option A is correct.

Question – 14

14.

Column-A Column-B
Number of factors of 20 that are smaller than 40 Number of multiples of 20 that are smaller than 45

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information

Factors of 20 = 1, 2, 4, 5, 10, 20
Multiples of 20 that are smaller than 45 = 20, 40
Option A is correct.

Question – 15

15. A teacher prepares a test having 5 objective-type questions. Each question has an incorrect and a correct option.?

Column-A Column-B
The number of correct ways in which the test can be answered The number of incorrect ways in which the test can be answered

• A. If the quantity on the left is greater

• B. If the quantity on the right is greater

• C. If both are equal

• D. If the relationship cannot be determined without further information