CMAT 2020: Previous Year Question Paper with Solutions

 Page 1


CMAT 2020
Quantitative Techniques and Data Interpretation
1. In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A    5041
B    5040
C    11670
D    11760
A n s w e r : D
Explanation:
Number of ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women
= 
= 
= 
= 
= 
=> Ans - (D)
2. What is the farthest distance between two points on a cylinder of: HEIGHT 8 and RADIUS 8 ?
A    
B    
C    
D    
A n s w e r : A
Explanation:
Height of cylinder = 8 units and radius = 8 units
=> Farthest distance = hypotenuse = 
=  units
=> Ans - (A)
3. Find the smallest number by which 2400 should be divided to make it a perfect cube.
C × 6
10
 C5
8
C × 4
10
C3
8
× 1×2×3×4
10×9×8×7
1×2×3
8×7×6
(10 × 3 × 7) × (8 × 7)
210 × 56 = 11760
8
5
16
5
8
2
8
3
(8) + (16)
2 2
8
5
  
.
Page 2


CMAT 2020
Quantitative Techniques and Data Interpretation
1. In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A    5041
B    5040
C    11670
D    11760
A n s w e r : D
Explanation:
Number of ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women
= 
= 
= 
= 
= 
=> Ans - (D)
2. What is the farthest distance between two points on a cylinder of: HEIGHT 8 and RADIUS 8 ?
A    
B    
C    
D    
A n s w e r : A
Explanation:
Height of cylinder = 8 units and radius = 8 units
=> Farthest distance = hypotenuse = 
=  units
=> Ans - (A)
3. Find the smallest number by which 2400 should be divided to make it a perfect cube.
C × 6
10
 C5
8
C × 4
10
C3
8
× 1×2×3×4
10×9×8×7
1×2×3
8×7×6
(10 × 3 × 7) × (8 × 7)
210 × 56 = 11760
8
5
16
5
8
2
8
3
(8) + (16)
2 2
8
5
  
.
A    
220
B    385
C    260
D    300
A n s w e r : D
Explanation:
Prime factorization of :
Now, to make it a perfect cube, we need to make the powers multiple of 3, and thus we need to divide it by = 
=> Ans - (D)
4. In a certain town, 40% of people have brown hair, 30% of people have brown eyes and 12% have both brown hair and brown
eyes.
How many people in town have neither brown hair nor brown eyes ?
A    44%
B    43%
C    41%
D    42%
A n s w e r : D
Explanation:
Let total number of people in the town = 
People who have both brown hair and eyes = 
=> People who have brown hair = 
=> 
Similarly, 
 People who have neither brown hair nor brown eyes = 
=> Ans - (D)
5. A company publishes to its customers that at a certain compound interest rate, a sum of money deposited by anyone will
become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will
it become 16 times ?
A    4 years
B    3.5 years
2400 = (2) ×
5
(3) × (5)
2
(2) ×
2
3 × (5) =
2
300
100 x
b = 12 x
a + b = 40 x
a = 28 x
c = 18 x
? 100 x - (12 x + 18 x + 28 x) = 42%
  
.
Page 3


CMAT 2020
Quantitative Techniques and Data Interpretation
1. In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A    5041
B    5040
C    11670
D    11760
A n s w e r : D
Explanation:
Number of ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women
= 
= 
= 
= 
= 
=> Ans - (D)
2. What is the farthest distance between two points on a cylinder of: HEIGHT 8 and RADIUS 8 ?
A    
B    
C    
D    
A n s w e r : A
Explanation:
Height of cylinder = 8 units and radius = 8 units
=> Farthest distance = hypotenuse = 
=  units
=> Ans - (A)
3. Find the smallest number by which 2400 should be divided to make it a perfect cube.
C × 6
10
 C5
8
C × 4
10
C3
8
× 1×2×3×4
10×9×8×7
1×2×3
8×7×6
(10 × 3 × 7) × (8 × 7)
210 × 56 = 11760
8
5
16
5
8
2
8
3
(8) + (16)
2 2
8
5
  
.
A    
220
B    385
C    260
D    300
A n s w e r : D
Explanation:
Prime factorization of :
Now, to make it a perfect cube, we need to make the powers multiple of 3, and thus we need to divide it by = 
=> Ans - (D)
4. In a certain town, 40% of people have brown hair, 30% of people have brown eyes and 12% have both brown hair and brown
eyes.
How many people in town have neither brown hair nor brown eyes ?
A    44%
B    43%
C    41%
D    42%
A n s w e r : D
Explanation:
Let total number of people in the town = 
People who have both brown hair and eyes = 
=> People who have brown hair = 
=> 
Similarly, 
 People who have neither brown hair nor brown eyes = 
=> Ans - (D)
5. A company publishes to its customers that at a certain compound interest rate, a sum of money deposited by anyone will
become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will
it become 16 times ?
A    4 years
B    3.5 years
2400 = (2) ×
5
(3) × (5)
2
(2) ×
2
3 × (5) =
2
300
100 x
b = 12 x
a + b = 40 x
a = 28 x
c = 18 x
? 100 x - (12 x + 18 x + 28 x) = 42%
  
.
C    
3 years
D    4.5 years
A n s w e r : A
Explanation:
If a sum of money becomes  times in  years, it will become  times in  years
=> 
Similarly, 
=> 
=> 
=>  years
=> Ans - (A)
6. The sum of two numbers is 135 and their HCF is 9. How many such pairs of numbers can be formed ?
A    2
B    5
C    4
D    6
A n s w e r : C
Explanation:
Let the two numbers be  and , where  and  are co prime numbers.
=> 
=> 
Now, pairs of natural numbers having sum 15 and co prime are = (1,14), (2,13), (4,11), (7,8)
Thus, 4 such pairs can be formed.
=> Ans - (C)
7. Simplify the following: 
A    0.03
B    0.135
C    0.982
D    9.37
A n s w e r : B
Explanation:
According to BODMAS, 
first Multiply the given numbers
0.3 x0.3= 0.09
0.03 x0.03=0.0009
0.6 x 0.03=0.018
simplifying this according to the given question,
x a y b
( x) =
a
1
( y)
b
1
(8) =
3
1
(16)
t
1
(2) =
3
3
(2)
t
4
1 = t
4
t = 4
9 x 9 y x y
9 x + 9 y = 135
x + y = = 9
135
15
0.54
0.3×0.3+0.03×0.03-0.6×0.03
  
.
Page 4


CMAT 2020
Quantitative Techniques and Data Interpretation
1. In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A    5041
B    5040
C    11670
D    11760
A n s w e r : D
Explanation:
Number of ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women
= 
= 
= 
= 
= 
=> Ans - (D)
2. What is the farthest distance between two points on a cylinder of: HEIGHT 8 and RADIUS 8 ?
A    
B    
C    
D    
A n s w e r : A
Explanation:
Height of cylinder = 8 units and radius = 8 units
=> Farthest distance = hypotenuse = 
=  units
=> Ans - (A)
3. Find the smallest number by which 2400 should be divided to make it a perfect cube.
C × 6
10
 C5
8
C × 4
10
C3
8
× 1×2×3×4
10×9×8×7
1×2×3
8×7×6
(10 × 3 × 7) × (8 × 7)
210 × 56 = 11760
8
5
16
5
8
2
8
3
(8) + (16)
2 2
8
5
  
.
A    
220
B    385
C    260
D    300
A n s w e r : D
Explanation:
Prime factorization of :
Now, to make it a perfect cube, we need to make the powers multiple of 3, and thus we need to divide it by = 
=> Ans - (D)
4. In a certain town, 40% of people have brown hair, 30% of people have brown eyes and 12% have both brown hair and brown
eyes.
How many people in town have neither brown hair nor brown eyes ?
A    44%
B    43%
C    41%
D    42%
A n s w e r : D
Explanation:
Let total number of people in the town = 
People who have both brown hair and eyes = 
=> People who have brown hair = 
=> 
Similarly, 
 People who have neither brown hair nor brown eyes = 
=> Ans - (D)
5. A company publishes to its customers that at a certain compound interest rate, a sum of money deposited by anyone will
become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will
it become 16 times ?
A    4 years
B    3.5 years
2400 = (2) ×
5
(3) × (5)
2
(2) ×
2
3 × (5) =
2
300
100 x
b = 12 x
a + b = 40 x
a = 28 x
c = 18 x
? 100 x - (12 x + 18 x + 28 x) = 42%
  
.
C    
3 years
D    4.5 years
A n s w e r : A
Explanation:
If a sum of money becomes  times in  years, it will become  times in  years
=> 
Similarly, 
=> 
=> 
=>  years
=> Ans - (A)
6. The sum of two numbers is 135 and their HCF is 9. How many such pairs of numbers can be formed ?
A    2
B    5
C    4
D    6
A n s w e r : C
Explanation:
Let the two numbers be  and , where  and  are co prime numbers.
=> 
=> 
Now, pairs of natural numbers having sum 15 and co prime are = (1,14), (2,13), (4,11), (7,8)
Thus, 4 such pairs can be formed.
=> Ans - (C)
7. Simplify the following: 
A    0.03
B    0.135
C    0.982
D    9.37
A n s w e r : B
Explanation:
According to BODMAS, 
first Multiply the given numbers
0.3 x0.3= 0.09
0.03 x0.03=0.0009
0.6 x 0.03=0.018
simplifying this according to the given question,
x a y b
( x) =
a
1
( y)
b
1
(8) =
3
1
(16)
t
1
(2) =
3
3
(2)
t
4
1 = t
4
t = 4
9 x 9 y x y
9 x + 9 y = 135
x + y = = 9
135
15
0.54
0.3×0.3+0.03×0.03-0.6×0.03
  
.
0.09-0.0009-0.018=0.0729
now 
=> 0.135
Therefore answer is option b 
    
8. The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of two numbers is 1 : 4, then the larger among two
numbers is:
A    28
B    48
C    88
D    84
A n s w e r : D
Explanation:
Let the two numbers be  and 
=> 
=> 
=> 
 Larger number = 
=> Ans - (D)
9. If x : y = 2 : 3, the value of (3x + 2y) : (2x + 5y) is:
A    
B    
C    
D    
A n s w e r : D
Explanation:
Let  and 
To find : 
= 
= 
=> Ans - (D)
10. The work done by a man, woman and child are in the ratio 3: 2:1. If daily wages of 20 men, 30 women and 36 children amount
to 78/-, what will be the wages of 15 men, 21 women and 30 children for 18 weeks ?
A    
7371/-
 0.54
 0.0729
x 4 x
x × 4 x = 84 × 21
x =
2
(21)
2
x = 21
? 4 × 21 = 84
25
12
27
11
15
11
19
12
x = 2 y = 3
2 x+5 y
3 x+2 y
2(2)+5(3)
3(2)+2(3)
19
12
  
.
Page 5


CMAT 2020
Quantitative Techniques and Data Interpretation
1. In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women ?
A    5041
B    5040
C    11670
D    11760
A n s w e r : D
Explanation:
Number of ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women
= 
= 
= 
= 
= 
=> Ans - (D)
2. What is the farthest distance between two points on a cylinder of: HEIGHT 8 and RADIUS 8 ?
A    
B    
C    
D    
A n s w e r : A
Explanation:
Height of cylinder = 8 units and radius = 8 units
=> Farthest distance = hypotenuse = 
=  units
=> Ans - (A)
3. Find the smallest number by which 2400 should be divided to make it a perfect cube.
C × 6
10
 C5
8
C × 4
10
C3
8
× 1×2×3×4
10×9×8×7
1×2×3
8×7×6
(10 × 3 × 7) × (8 × 7)
210 × 56 = 11760
8
5
16
5
8
2
8
3
(8) + (16)
2 2
8
5
  
.
A    
220
B    385
C    260
D    300
A n s w e r : D
Explanation:
Prime factorization of :
Now, to make it a perfect cube, we need to make the powers multiple of 3, and thus we need to divide it by = 
=> Ans - (D)
4. In a certain town, 40% of people have brown hair, 30% of people have brown eyes and 12% have both brown hair and brown
eyes.
How many people in town have neither brown hair nor brown eyes ?
A    44%
B    43%
C    41%
D    42%
A n s w e r : D
Explanation:
Let total number of people in the town = 
People who have both brown hair and eyes = 
=> People who have brown hair = 
=> 
Similarly, 
 People who have neither brown hair nor brown eyes = 
=> Ans - (D)
5. A company publishes to its customers that at a certain compound interest rate, a sum of money deposited by anyone will
become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will
it become 16 times ?
A    4 years
B    3.5 years
2400 = (2) ×
5
(3) × (5)
2
(2) ×
2
3 × (5) =
2
300
100 x
b = 12 x
a + b = 40 x
a = 28 x
c = 18 x
? 100 x - (12 x + 18 x + 28 x) = 42%
  
.
C    
3 years
D    4.5 years
A n s w e r : A
Explanation:
If a sum of money becomes  times in  years, it will become  times in  years
=> 
Similarly, 
=> 
=> 
=>  years
=> Ans - (A)
6. The sum of two numbers is 135 and their HCF is 9. How many such pairs of numbers can be formed ?
A    2
B    5
C    4
D    6
A n s w e r : C
Explanation:
Let the two numbers be  and , where  and  are co prime numbers.
=> 
=> 
Now, pairs of natural numbers having sum 15 and co prime are = (1,14), (2,13), (4,11), (7,8)
Thus, 4 such pairs can be formed.
=> Ans - (C)
7. Simplify the following: 
A    0.03
B    0.135
C    0.982
D    9.37
A n s w e r : B
Explanation:
According to BODMAS, 
first Multiply the given numbers
0.3 x0.3= 0.09
0.03 x0.03=0.0009
0.6 x 0.03=0.018
simplifying this according to the given question,
x a y b
( x) =
a
1
( y)
b
1
(8) =
3
1
(16)
t
1
(2) =
3
3
(2)
t
4
1 = t
4
t = 4
9 x 9 y x y
9 x + 9 y = 135
x + y = = 9
135
15
0.54
0.3×0.3+0.03×0.03-0.6×0.03
  
.
0.09-0.0009-0.018=0.0729
now 
=> 0.135
Therefore answer is option b 
    
8. The LCM and HCF of two numbers are 84 and 21 respectively. If the ratio of two numbers is 1 : 4, then the larger among two
numbers is:
A    28
B    48
C    88
D    84
A n s w e r : D
Explanation:
Let the two numbers be  and 
=> 
=> 
=> 
 Larger number = 
=> Ans - (D)
9. If x : y = 2 : 3, the value of (3x + 2y) : (2x + 5y) is:
A    
B    
C    
D    
A n s w e r : D
Explanation:
Let  and 
To find : 
= 
= 
=> Ans - (D)
10. The work done by a man, woman and child are in the ratio 3: 2:1. If daily wages of 20 men, 30 women and 36 children amount
to 78/-, what will be the wages of 15 men, 21 women and 30 children for 18 weeks ?
A    
7371/-
 0.54
 0.0729
x 4 x
x × 4 x = 84 × 21
x =
2
(21)
2
x = 21
? 4 × 21 = 84
25
12
27
11
15
11
19
12
x = 2 y = 3
2 x+5 y
3 x+2 y
2(2)+5(3)
3(2)+2(3)
19
12
  
.
B    
8645/-
C    7532/-
D    9000/-
A n s w e r : A
Explanation:
Let the efficiency of a man, woman and child be  espectively.
Thus, 1 day wage = 
=> 
=> 
 Wages of 15 men, 21 women and 30 children for 18 weeks = 
= 
=  
=> Ans - (A)
     
11. X and Y are running towards each other from their houses. X can reach Y’s house in 25 minutes which is half the time taken by
Y to run from his house to X’s house. If the two start to run towards each otherat the same time, then how much more time it
will be required by Y to reach the middle of houses ?
A    18 min.
B    25 min.
C    50 min.
D    12.5 min.
A n s w e r : D
Explanation:
Time taken by X to reach Y's house = 25 minutes and by Y to reach X's house = 50 min
Ratio of time taken = 
 speed is inversely proportional to time, let speed of X =  km/min and speed of Y =  km/min and distance between their houses = 
 km
Using, speed = distance/time
=> 
=>  -------------(i)
Now, time taken by Y to travel  km, i.e. mid way = 
=  minutes
Now, time taken by X to travel  km, i.e. mid way = 
=  minutes
So, the correct answer is  minutes
=> Ans - (D)
3 x, 2 x, x
(3 x × 20) + (2 x × 30) + ( x × 36) = 78
156 x = 78
x = 2
1
? [(15 × 3 x) + (21 × 2 x) + (30 × x)] × 18 × 7
117 × × 2
1
126
117 × 63 = R s. 7, 371
1 : 2
? 2 x x
2 d
x = = 50
2 d
25
d
= x
d
25
d x
d
25
d 2 x
d
12.5
25 - 12.5 = 12.5
n d r d
  
.