CMAT 2022: Previous Year Question Paper with Solutions

 Page 1


CMAT 2022
Quantitative Techniques and Data Interpretation
1. In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batch is 62.
Average Marks of Boys will be:
A    61
B    63
C    62
D    65
A n s w e r : D
Explanation:
Let the number of boys be 4x and number of girls be 6x
Given, 4x+6x = 50
                   x = 5
Number of boys = 20 and number of girls = 30
Average marks of girls = 60
Total marks scored by girls = 60 30 = 1800
Average marks score by batch = 62
Total marks scored by batch = 62 50 = 3100
Marks scored by boys = 3100 - 1800 = 1300
Average marks of boys =  = 65
Answer is option D.
2. Four sheep farmers rented a pasture, Anil grazed his 24 sheep for 3 months, Bimal 10 sheep for 5 months, Champak 35 sheep
for 4 months and Damodar 21 sheep for 3 months,. If Anil’s share of rent is Rs. 720, find the total rent of the pasture :
A    Rs.3,200
B    Rs.3,250
C    Rs.2,300
D    Rs.4,000
A n s w e r : B
Explanation:
A : B : C : D = 24( ) : 10( ) : 35( ) : 21( )
A : B : C ; D = 6 :  :  : 
A : B: C : D = 72 : 50 : 140 : 63
Anil's rent =  Total rent
720 =  T
T = Rs 3,250
Answer is option B.
× 
× 
20
1300
12
3
12
5
12
4
12
3
6
25
3
35
4
21
× 72+50+140+63
72
× 325
72
  
.
Page 2


CMAT 2022
Quantitative Techniques and Data Interpretation
1. In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batch is 62.
Average Marks of Boys will be:
A    61
B    63
C    62
D    65
A n s w e r : D
Explanation:
Let the number of boys be 4x and number of girls be 6x
Given, 4x+6x = 50
                   x = 5
Number of boys = 20 and number of girls = 30
Average marks of girls = 60
Total marks scored by girls = 60 30 = 1800
Average marks score by batch = 62
Total marks scored by batch = 62 50 = 3100
Marks scored by boys = 3100 - 1800 = 1300
Average marks of boys =  = 65
Answer is option D.
2. Four sheep farmers rented a pasture, Anil grazed his 24 sheep for 3 months, Bimal 10 sheep for 5 months, Champak 35 sheep
for 4 months and Damodar 21 sheep for 3 months,. If Anil’s share of rent is Rs. 720, find the total rent of the pasture :
A    Rs.3,200
B    Rs.3,250
C    Rs.2,300
D    Rs.4,000
A n s w e r : B
Explanation:
A : B : C : D = 24( ) : 10( ) : 35( ) : 21( )
A : B : C ; D = 6 :  :  : 
A : B: C : D = 72 : 50 : 140 : 63
Anil's rent =  Total rent
720 =  T
T = Rs 3,250
Answer is option B.
× 
× 
20
1300
12
3
12
5
12
4
12
3
6
25
3
35
4
21
× 72+50+140+63
72
× 325
72
  
.
3. A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :
A    17 m
B    18 cm
C    15 cm
D    20 cm
A n s w e r : B
Explanation:
Volume of copper wire melted will be equal to volume of sphere.
Volume of copper wire = Area  length = 
Let the radius of sphere be r
 = 729
r = 9 cm
Diameter of sphere = 2(9) = 18 cm
Answer is option B.
4. If the cost price is 80% of the selling price, then what is the profit in percentage?
A    20%
B    25%
C    16%
D    22.5%
A n s w e r : B
Explanation:
Given, cost price is 80% of selling price
C.P = 0.8 S.P
Profit = 
         = 
         =
         = 25%
Answer is option B
5. In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls
and 1 green ball is :
A    
B    
C    
× p × ( 10
2
)
2
24300 c m
3
p r = 3
4
3  
p × ( 10
2
)
2
24300 c m
3
r
3
 × C. P
 S. P - C. P
100
 × 0.8 S. P
 S. P - 0.8 S. P
100
 × 0.8
0.2
100
46
21
117
25
25
3
1
  
.
Page 3


CMAT 2022
Quantitative Techniques and Data Interpretation
1. In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batch is 62.
Average Marks of Boys will be:
A    61
B    63
C    62
D    65
A n s w e r : D
Explanation:
Let the number of boys be 4x and number of girls be 6x
Given, 4x+6x = 50
                   x = 5
Number of boys = 20 and number of girls = 30
Average marks of girls = 60
Total marks scored by girls = 60 30 = 1800
Average marks score by batch = 62
Total marks scored by batch = 62 50 = 3100
Marks scored by boys = 3100 - 1800 = 1300
Average marks of boys =  = 65
Answer is option D.
2. Four sheep farmers rented a pasture, Anil grazed his 24 sheep for 3 months, Bimal 10 sheep for 5 months, Champak 35 sheep
for 4 months and Damodar 21 sheep for 3 months,. If Anil’s share of rent is Rs. 720, find the total rent of the pasture :
A    Rs.3,200
B    Rs.3,250
C    Rs.2,300
D    Rs.4,000
A n s w e r : B
Explanation:
A : B : C : D = 24( ) : 10( ) : 35( ) : 21( )
A : B : C ; D = 6 :  :  : 
A : B: C : D = 72 : 50 : 140 : 63
Anil's rent =  Total rent
720 =  T
T = Rs 3,250
Answer is option B.
× 
× 
20
1300
12
3
12
5
12
4
12
3
6
25
3
35
4
21
× 72+50+140+63
72
× 325
72
  
.
3. A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :
A    17 m
B    18 cm
C    15 cm
D    20 cm
A n s w e r : B
Explanation:
Volume of copper wire melted will be equal to volume of sphere.
Volume of copper wire = Area  length = 
Let the radius of sphere be r
 = 729
r = 9 cm
Diameter of sphere = 2(9) = 18 cm
Answer is option B.
4. If the cost price is 80% of the selling price, then what is the profit in percentage?
A    20%
B    25%
C    16%
D    22.5%
A n s w e r : B
Explanation:
Given, cost price is 80% of selling price
C.P = 0.8 S.P
Profit = 
         = 
         =
         = 25%
Answer is option B
5. In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls
and 1 green ball is :
A    
B    
C    
× p × ( 10
2
)
2
24300 c m
3
p r = 3
4
3  
p × ( 10
2
)
2
24300 c m
3
r
3
 × C. P
 S. P - C. P
100
 × 0.8 S. P
 S. P - 0.8 S. P
100
 × 0.8
0.2
100
46
21
117
25
25
3
1
  
.
D    
A n s w e r : A
Explanation:
Number of ways of selecting 2 red balls and 1 green ball = 
Number of ways of selecting 3 balls = 
Probability of selecting 2 red balls and 1 green ball =  = 
Answer is option A.
6. With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 30 km/hr, it is late
by 36 minutes. The total distance travelled by train is :
A    72 km
B    78 km
C    60 km
D    40 km
A n s w e r : A
Explanation:
Let us consider with average speed of 40 km/hr, train reached its destination in time t hrs
with average speed of 30 km/hr, it takes t + hrs
Distance will be same in both the cases
40t = 30t + 18
10t = 18
t = 
Distance = 40t = 40 = 72 km
Answer is option A.
7. A man borrows Rs 4000 at 15% compound interest. At the end of each year he pays back Rs 1500. How much amount is required
to pay at the end of third year to clear all his dues :
A    Rs.775.75
B    Rs.973.85
C    Rs.1500
D    Rs.874.75
A n s w e r : D
Explanation:
Time value of money Rs 4,000 at the end of 3 years = 4,000 = Rs 6083.5
Value of first installment at the end of 3 years = 1500 = Rs 1983.75
Value of second installment at the end of 3 years = 1500 = Rs 1725
Value of third installment = 1500
Let us assume he has to pay Rs. x to clear all his dues
1983.75 + 1725 + 1500 + x = 6083.5
50
1
15 . 10 C2 C1
25 C3
 
25
C3
15 .10
C2 C1
46
21
60
36
10
18
× 10
18
1 + ( 100
15
)
3
1 + ( 100
15
)
2
1 + ( 100
15
)
  
.
Page 4


CMAT 2022
Quantitative Techniques and Data Interpretation
1. In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batch is 62.
Average Marks of Boys will be:
A    61
B    63
C    62
D    65
A n s w e r : D
Explanation:
Let the number of boys be 4x and number of girls be 6x
Given, 4x+6x = 50
                   x = 5
Number of boys = 20 and number of girls = 30
Average marks of girls = 60
Total marks scored by girls = 60 30 = 1800
Average marks score by batch = 62
Total marks scored by batch = 62 50 = 3100
Marks scored by boys = 3100 - 1800 = 1300
Average marks of boys =  = 65
Answer is option D.
2. Four sheep farmers rented a pasture, Anil grazed his 24 sheep for 3 months, Bimal 10 sheep for 5 months, Champak 35 sheep
for 4 months and Damodar 21 sheep for 3 months,. If Anil’s share of rent is Rs. 720, find the total rent of the pasture :
A    Rs.3,200
B    Rs.3,250
C    Rs.2,300
D    Rs.4,000
A n s w e r : B
Explanation:
A : B : C : D = 24( ) : 10( ) : 35( ) : 21( )
A : B : C ; D = 6 :  :  : 
A : B: C : D = 72 : 50 : 140 : 63
Anil's rent =  Total rent
720 =  T
T = Rs 3,250
Answer is option B.
× 
× 
20
1300
12
3
12
5
12
4
12
3
6
25
3
35
4
21
× 72+50+140+63
72
× 325
72
  
.
3. A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :
A    17 m
B    18 cm
C    15 cm
D    20 cm
A n s w e r : B
Explanation:
Volume of copper wire melted will be equal to volume of sphere.
Volume of copper wire = Area  length = 
Let the radius of sphere be r
 = 729
r = 9 cm
Diameter of sphere = 2(9) = 18 cm
Answer is option B.
4. If the cost price is 80% of the selling price, then what is the profit in percentage?
A    20%
B    25%
C    16%
D    22.5%
A n s w e r : B
Explanation:
Given, cost price is 80% of selling price
C.P = 0.8 S.P
Profit = 
         = 
         =
         = 25%
Answer is option B
5. In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls
and 1 green ball is :
A    
B    
C    
× p × ( 10
2
)
2
24300 c m
3
p r = 3
4
3  
p × ( 10
2
)
2
24300 c m
3
r
3
 × C. P
 S. P - C. P
100
 × 0.8 S. P
 S. P - 0.8 S. P
100
 × 0.8
0.2
100
46
21
117
25
25
3
1
  
.
D    
A n s w e r : A
Explanation:
Number of ways of selecting 2 red balls and 1 green ball = 
Number of ways of selecting 3 balls = 
Probability of selecting 2 red balls and 1 green ball =  = 
Answer is option A.
6. With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 30 km/hr, it is late
by 36 minutes. The total distance travelled by train is :
A    72 km
B    78 km
C    60 km
D    40 km
A n s w e r : A
Explanation:
Let us consider with average speed of 40 km/hr, train reached its destination in time t hrs
with average speed of 30 km/hr, it takes t + hrs
Distance will be same in both the cases
40t = 30t + 18
10t = 18
t = 
Distance = 40t = 40 = 72 km
Answer is option A.
7. A man borrows Rs 4000 at 15% compound interest. At the end of each year he pays back Rs 1500. How much amount is required
to pay at the end of third year to clear all his dues :
A    Rs.775.75
B    Rs.973.85
C    Rs.1500
D    Rs.874.75
A n s w e r : D
Explanation:
Time value of money Rs 4,000 at the end of 3 years = 4,000 = Rs 6083.5
Value of first installment at the end of 3 years = 1500 = Rs 1983.75
Value of second installment at the end of 3 years = 1500 = Rs 1725
Value of third installment = 1500
Let us assume he has to pay Rs. x to clear all his dues
1983.75 + 1725 + 1500 + x = 6083.5
50
1
15 . 10 C2 C1
25 C3
 
25
C3
15 .10
C2 C1
46
21
60
36
10
18
× 10
18
1 + ( 100
15
)
3
1 + ( 100
15
)
2
1 + ( 100
15
)
  
.
x = Rs 874.75
Answer is option D.
    
8. The following pie chart embodies the details about the per cent production by seven different companies A-G with the total
production for all companies at 1500 units.
(A) Companies A & G are producing more than 500 units
(B) Companies B & F are producing less than 250 units
(C) Companies C & E account for 705 units
(D) Companies D & G are producing less than 200 units
(E) Companies E, F & G account for 545 units
Choose the correct answer from the options given below:
A    Only (A) & (B) are true
B    Only (B) & (C) are true
C    Only (D) & (E) are true
D    Only (A) & (E) are true
A n s w e r : B
Explanation:
Total production = 1500 units
A) A and G production = 240 + 180 = 420 (not greater than 500)
B) B and F production = 165 + 75 = 240 ( is less than 250)
C) C and E production = 315 + 390 = 705 
D) D and G production = 135 +180 = 315 ( not less than 200)
E) E, F and G production = 390 + 75 + 180 = 645 ( not equal to 545)
Only (B) and (C) are true.
Answer is option B.
  
.
Page 5


CMAT 2022
Quantitative Techniques and Data Interpretation
1. In a batch of 50 students has ratio of Boys to Girls as 4:6. Average marks of Girls are 60 and Average marks of the batch is 62.
Average Marks of Boys will be:
A    61
B    63
C    62
D    65
A n s w e r : D
Explanation:
Let the number of boys be 4x and number of girls be 6x
Given, 4x+6x = 50
                   x = 5
Number of boys = 20 and number of girls = 30
Average marks of girls = 60
Total marks scored by girls = 60 30 = 1800
Average marks score by batch = 62
Total marks scored by batch = 62 50 = 3100
Marks scored by boys = 3100 - 1800 = 1300
Average marks of boys =  = 65
Answer is option D.
2. Four sheep farmers rented a pasture, Anil grazed his 24 sheep for 3 months, Bimal 10 sheep for 5 months, Champak 35 sheep
for 4 months and Damodar 21 sheep for 3 months,. If Anil’s share of rent is Rs. 720, find the total rent of the pasture :
A    Rs.3,200
B    Rs.3,250
C    Rs.2,300
D    Rs.4,000
A n s w e r : B
Explanation:
A : B : C : D = 24( ) : 10( ) : 35( ) : 21( )
A : B : C ; D = 6 :  :  : 
A : B: C : D = 72 : 50 : 140 : 63
Anil's rent =  Total rent
720 =  T
T = Rs 3,250
Answer is option B.
× 
× 
20
1300
12
3
12
5
12
4
12
3
6
25
3
35
4
21
× 72+50+140+63
72
× 325
72
  
.
3. A copper wire having length of 243m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere :
A    17 m
B    18 cm
C    15 cm
D    20 cm
A n s w e r : B
Explanation:
Volume of copper wire melted will be equal to volume of sphere.
Volume of copper wire = Area  length = 
Let the radius of sphere be r
 = 729
r = 9 cm
Diameter of sphere = 2(9) = 18 cm
Answer is option B.
4. If the cost price is 80% of the selling price, then what is the profit in percentage?
A    20%
B    25%
C    16%
D    22.5%
A n s w e r : B
Explanation:
Given, cost price is 80% of selling price
C.P = 0.8 S.P
Profit = 
         = 
         =
         = 25%
Answer is option B
5. In a bag there are 15 red balls and 10 green balls. Three balls are selected at random. The probability of selecting 2 red balls
and 1 green ball is :
A    
B    
C    
× p × ( 10
2
)
2
24300 c m
3
p r = 3
4
3  
p × ( 10
2
)
2
24300 c m
3
r
3
 × C. P
 S. P - C. P
100
 × 0.8 S. P
 S. P - 0.8 S. P
100
 × 0.8
0.2
100
46
21
117
25
25
3
1
  
.
D    
A n s w e r : A
Explanation:
Number of ways of selecting 2 red balls and 1 green ball = 
Number of ways of selecting 3 balls = 
Probability of selecting 2 red balls and 1 green ball =  = 
Answer is option A.
6. With an average speed of 40 km/hr, a train reaches its destination in time. If it goes with an average speed of 30 km/hr, it is late
by 36 minutes. The total distance travelled by train is :
A    72 km
B    78 km
C    60 km
D    40 km
A n s w e r : A
Explanation:
Let us consider with average speed of 40 km/hr, train reached its destination in time t hrs
with average speed of 30 km/hr, it takes t + hrs
Distance will be same in both the cases
40t = 30t + 18
10t = 18
t = 
Distance = 40t = 40 = 72 km
Answer is option A.
7. A man borrows Rs 4000 at 15% compound interest. At the end of each year he pays back Rs 1500. How much amount is required
to pay at the end of third year to clear all his dues :
A    Rs.775.75
B    Rs.973.85
C    Rs.1500
D    Rs.874.75
A n s w e r : D
Explanation:
Time value of money Rs 4,000 at the end of 3 years = 4,000 = Rs 6083.5
Value of first installment at the end of 3 years = 1500 = Rs 1983.75
Value of second installment at the end of 3 years = 1500 = Rs 1725
Value of third installment = 1500
Let us assume he has to pay Rs. x to clear all his dues
1983.75 + 1725 + 1500 + x = 6083.5
50
1
15 . 10 C2 C1
25 C3
 
25
C3
15 .10
C2 C1
46
21
60
36
10
18
× 10
18
1 + ( 100
15
)
3
1 + ( 100
15
)
2
1 + ( 100
15
)
  
.
x = Rs 874.75
Answer is option D.
    
8. The following pie chart embodies the details about the per cent production by seven different companies A-G with the total
production for all companies at 1500 units.
(A) Companies A & G are producing more than 500 units
(B) Companies B & F are producing less than 250 units
(C) Companies C & E account for 705 units
(D) Companies D & G are producing less than 200 units
(E) Companies E, F & G account for 545 units
Choose the correct answer from the options given below:
A    Only (A) & (B) are true
B    Only (B) & (C) are true
C    Only (D) & (E) are true
D    Only (A) & (E) are true
A n s w e r : B
Explanation:
Total production = 1500 units
A) A and G production = 240 + 180 = 420 (not greater than 500)
B) B and F production = 165 + 75 = 240 ( is less than 250)
C) C and E production = 315 + 390 = 705 
D) D and G production = 135 +180 = 315 ( not less than 200)
E) E, F and G production = 390 + 75 + 180 = 645 ( not equal to 545)
Only (B) and (C) are true.
Answer is option B.
  
.
9. In a local election between two candidates, one candidate got 55% of the total valid votes and was declared as winner. 15% of
the votes were invalid. If the total number of votes polled were 15200, what were the valid votes of the loser :
A    6840
B    5800
C    5814
D    6216
A n s w e r : C
Explanation:
Total number of votes = 15200
15% of total votes are invalid, this implies 85% are valid.
55% of valid votes are secured by winner, this implies 45% of valid votes are secured by loser
Voted secured by loser =  = 5814
Answer is option C.
10. If  is a positive fraction and  is a negative fraction then which of the following statements are true
(A)  is positive
(B)  is positive
(C)  is negative
(D)  is positive
(E)  is positive
Choose the correct answer from the options given below:
A    Only (A) & (B) are true
B    Only (B) & (C) are true
C    Only (D) & (E) are true
D    Only (A) & (E) are true
A n s w e r : B
Explanation:
It is given that  is positive and  is negative, this implies that x is positive and y is negative.
A)  is positive, we know x is positive, and y is negative, but we cannot conclude which value is greater. Therefore, this may or
may not be true.
B) is positive; we know that x is positive and y is negative. So this statement is definitely true.
C) = -( )
As  is positive,  is negative and statement is true.
D)  is negative as x is positive and y is negative. Therefore, the statement is false.
E) is positive only when , but we cannot conclude which value is greater. Therefore, this may or may not be true.
Only (B) and (C) are true.
Answer is option B
× 100
45
× 100
85
15200
x
1
y
1
+ x
1
y
1
- x
1
y
1
x y
x- y
x y
1
- x
2
1
y
2
1
x
1
y
1
 + x
1
y
1
- x
1
y
1
 
x y
 x- y
- x
1
y
1
- x
1
y
1
 
x y
 x- y
x y
1
- x
2
1
y
2
1
y >
2
x
2
  
.