CMAT 2021 Slot - 1: Previous Year Question Paper with Solutions

 Page 1


CMAT 2021 Slot-1
Quantitative Techniques and Data Interpretation
1. Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:
A    4 hours
B    6 hours
C    10 hours
D    2 hours
A n s w e r : A
Explanation:
Let the volume be 20 units 
So A fills at 4 units/hr 
B fills at 1 unit/hr
Now together they fill 4+1 = 5 units/ hour
Now time taken to fill completely : 20/5 = 4 hrs
2. In June-2020, the ratio of boys to girls in a college was 3 : 2. In September-2020, there were 80 fewer boys and 20 fewer girls in
the college and the ratio of boys to girls was 7 : 5. What was the total number of students in the college in June-2020?
A    1000
B    1100
C    1200
D    1300
A n s w e r : D
Explanation:
In June 2020 
Let the number of boys be 3x 
So number of girls will be 2x
Now number of boys in September 2020: 3x-80 and girls in September 2020 : 2x-20
Now as per given 3x-80:2x-20 =7:5
we get 15x-400 =14x-140
we get x=260
So number of students in June 2020 = 3x+2x =5x = 1300
3. M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is  of M. How many such M's are
possible?
A    10
B    9
C    8
D    7
A n s w e r : D
Explanation:
According to question,
9
1
t h
  
.
Page 2


CMAT 2021 Slot-1
Quantitative Techniques and Data Interpretation
1. Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:
A    4 hours
B    6 hours
C    10 hours
D    2 hours
A n s w e r : A
Explanation:
Let the volume be 20 units 
So A fills at 4 units/hr 
B fills at 1 unit/hr
Now together they fill 4+1 = 5 units/ hour
Now time taken to fill completely : 20/5 = 4 hrs
2. In June-2020, the ratio of boys to girls in a college was 3 : 2. In September-2020, there were 80 fewer boys and 20 fewer girls in
the college and the ratio of boys to girls was 7 : 5. What was the total number of students in the college in June-2020?
A    1000
B    1100
C    1200
D    1300
A n s w e r : D
Explanation:
In June 2020 
Let the number of boys be 3x 
So number of girls will be 2x
Now number of boys in September 2020: 3x-80 and girls in September 2020 : 2x-20
Now as per given 3x-80:2x-20 =7:5
we get 15x-400 =14x-140
we get x=260
So number of students in June 2020 = 3x+2x =5x = 1300
3. M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is  of M. How many such M's are
possible?
A    10
B    9
C    8
D    7
A n s w e r : D
Explanation:
According to question,
9
1
t h
  
.
Number AXYZ/9 = XYZ
It can be written as
A000/9 + XYZ/9 = XYZ
A000/9 + XYZ/9 = 9XYZ/9
A000/9 = 8XYZ/9
A000 = 8XYZ
We have to find the maximum value of A so that when A000 is divided by 8 gives three digit numbers.
7000/8= 875 and 8000/8=1000.
So, answer is 7.
4. L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together
in 90 days. In what time can L alone complete the work?
A    150 days
B    80 days
C    100 days
D    120 days
A n s w e r : D
Explanation:
Let L does a units of work/day 
M does b units of work/ day 
N does c units of work/ day 
Now as per given conditions :
Let work be W 
So we get 
W = 72(a+b) =120(b+c) =90(a+c)
we get 
6a+6b = 10b +10c 
we get 6a-4b-10c=0   (1)
also 
4a+4b =5a+5c
we get a-4b+5c =0   (2)
From (1) and (2) 
we get a=3 , b=2 and c=1 
Now therefore W = 360
Now time taken by L alone to complete the work = 360/3 = 120 days
5. Given below are two statements
Statement I : The set of numbers(5,6, 7, p, 6, 7, 8, q) has an arithmetic mean of 6 and mode (most frequently occurring number)
of 7. Then .
Statement II: Let p and q be two positive integers such that . Then .
In light of the above statements, choose the correct answer from the options given below
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement I is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : B
p × q = 16
p + q + p × q = 94 p + q = 20
  
.
Page 3


CMAT 2021 Slot-1
Quantitative Techniques and Data Interpretation
1. Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:
A    4 hours
B    6 hours
C    10 hours
D    2 hours
A n s w e r : A
Explanation:
Let the volume be 20 units 
So A fills at 4 units/hr 
B fills at 1 unit/hr
Now together they fill 4+1 = 5 units/ hour
Now time taken to fill completely : 20/5 = 4 hrs
2. In June-2020, the ratio of boys to girls in a college was 3 : 2. In September-2020, there were 80 fewer boys and 20 fewer girls in
the college and the ratio of boys to girls was 7 : 5. What was the total number of students in the college in June-2020?
A    1000
B    1100
C    1200
D    1300
A n s w e r : D
Explanation:
In June 2020 
Let the number of boys be 3x 
So number of girls will be 2x
Now number of boys in September 2020: 3x-80 and girls in September 2020 : 2x-20
Now as per given 3x-80:2x-20 =7:5
we get 15x-400 =14x-140
we get x=260
So number of students in June 2020 = 3x+2x =5x = 1300
3. M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is  of M. How many such M's are
possible?
A    10
B    9
C    8
D    7
A n s w e r : D
Explanation:
According to question,
9
1
t h
  
.
Number AXYZ/9 = XYZ
It can be written as
A000/9 + XYZ/9 = XYZ
A000/9 + XYZ/9 = 9XYZ/9
A000/9 = 8XYZ/9
A000 = 8XYZ
We have to find the maximum value of A so that when A000 is divided by 8 gives three digit numbers.
7000/8= 875 and 8000/8=1000.
So, answer is 7.
4. L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together
in 90 days. In what time can L alone complete the work?
A    150 days
B    80 days
C    100 days
D    120 days
A n s w e r : D
Explanation:
Let L does a units of work/day 
M does b units of work/ day 
N does c units of work/ day 
Now as per given conditions :
Let work be W 
So we get 
W = 72(a+b) =120(b+c) =90(a+c)
we get 
6a+6b = 10b +10c 
we get 6a-4b-10c=0   (1)
also 
4a+4b =5a+5c
we get a-4b+5c =0   (2)
From (1) and (2) 
we get a=3 , b=2 and c=1 
Now therefore W = 360
Now time taken by L alone to complete the work = 360/3 = 120 days
5. Given below are two statements
Statement I : The set of numbers(5,6, 7, p, 6, 7, 8, q) has an arithmetic mean of 6 and mode (most frequently occurring number)
of 7. Then .
Statement II: Let p and q be two positive integers such that . Then .
In light of the above statements, choose the correct answer from the options given below
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement I is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : B
p × q = 16
p + q + p × q = 94 p + q = 20
  
.
Explanation:
we get 39+p+q =48
so p+q =9 
Now pq cannot be 16 for any value of p and q so 1 is false 
p+q+pq=94
we get p+q+pq+1 =95
we get (p+1)(q+1) =95
we get (0,94) ; (4,18)
So p+q is not 20 
Hence statement 2 is false
6. A milkman adds 10 litres of water to 90 litres of milk. After selling  of the total quantity, he adds water equal to the quantity
he sold. The proportion of water to milk he sells now would be:
A    72 : 28
B    28 : 72
C    20 : 80
D    30 : 70
A n s w e r : B
Explanation:
Initially Milkman has 90 liters of milk
Now amount of water added = 10 liters 
So total quantity becomes : 100 liters 
He sold 1/5 of quantity 
so he sold 2 liters of water and 18 liters of milk (A total of 20 liters is sold )
Now he is left with 10-2 = 8 liters of water  and 90-18 = 72 liters of milk.
Now he adds 20 liters of water 
so the amount of milk and water with him will be : 72 and 28 respectively.
7. In a  and  are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a 
and the area of a  is:
A    1:4
B    1:2
C    2:3
D    4:5
A n s w e r : A
Explanation:
We are given :
5
1
t h
? A B C, D, E F ? D E F
? A B C
  
.
Page 4


CMAT 2021 Slot-1
Quantitative Techniques and Data Interpretation
1. Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:
A    4 hours
B    6 hours
C    10 hours
D    2 hours
A n s w e r : A
Explanation:
Let the volume be 20 units 
So A fills at 4 units/hr 
B fills at 1 unit/hr
Now together they fill 4+1 = 5 units/ hour
Now time taken to fill completely : 20/5 = 4 hrs
2. In June-2020, the ratio of boys to girls in a college was 3 : 2. In September-2020, there were 80 fewer boys and 20 fewer girls in
the college and the ratio of boys to girls was 7 : 5. What was the total number of students in the college in June-2020?
A    1000
B    1100
C    1200
D    1300
A n s w e r : D
Explanation:
In June 2020 
Let the number of boys be 3x 
So number of girls will be 2x
Now number of boys in September 2020: 3x-80 and girls in September 2020 : 2x-20
Now as per given 3x-80:2x-20 =7:5
we get 15x-400 =14x-140
we get x=260
So number of students in June 2020 = 3x+2x =5x = 1300
3. M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is  of M. How many such M's are
possible?
A    10
B    9
C    8
D    7
A n s w e r : D
Explanation:
According to question,
9
1
t h
  
.
Number AXYZ/9 = XYZ
It can be written as
A000/9 + XYZ/9 = XYZ
A000/9 + XYZ/9 = 9XYZ/9
A000/9 = 8XYZ/9
A000 = 8XYZ
We have to find the maximum value of A so that when A000 is divided by 8 gives three digit numbers.
7000/8= 875 and 8000/8=1000.
So, answer is 7.
4. L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together
in 90 days. In what time can L alone complete the work?
A    150 days
B    80 days
C    100 days
D    120 days
A n s w e r : D
Explanation:
Let L does a units of work/day 
M does b units of work/ day 
N does c units of work/ day 
Now as per given conditions :
Let work be W 
So we get 
W = 72(a+b) =120(b+c) =90(a+c)
we get 
6a+6b = 10b +10c 
we get 6a-4b-10c=0   (1)
also 
4a+4b =5a+5c
we get a-4b+5c =0   (2)
From (1) and (2) 
we get a=3 , b=2 and c=1 
Now therefore W = 360
Now time taken by L alone to complete the work = 360/3 = 120 days
5. Given below are two statements
Statement I : The set of numbers(5,6, 7, p, 6, 7, 8, q) has an arithmetic mean of 6 and mode (most frequently occurring number)
of 7. Then .
Statement II: Let p and q be two positive integers such that . Then .
In light of the above statements, choose the correct answer from the options given below
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement I is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : B
p × q = 16
p + q + p × q = 94 p + q = 20
  
.
Explanation:
we get 39+p+q =48
so p+q =9 
Now pq cannot be 16 for any value of p and q so 1 is false 
p+q+pq=94
we get p+q+pq+1 =95
we get (p+1)(q+1) =95
we get (0,94) ; (4,18)
So p+q is not 20 
Hence statement 2 is false
6. A milkman adds 10 litres of water to 90 litres of milk. After selling  of the total quantity, he adds water equal to the quantity
he sold. The proportion of water to milk he sells now would be:
A    72 : 28
B    28 : 72
C    20 : 80
D    30 : 70
A n s w e r : B
Explanation:
Initially Milkman has 90 liters of milk
Now amount of water added = 10 liters 
So total quantity becomes : 100 liters 
He sold 1/5 of quantity 
so he sold 2 liters of water and 18 liters of milk (A total of 20 liters is sold )
Now he is left with 10-2 = 8 liters of water  and 90-18 = 72 liters of milk.
Now he adds 20 liters of water 
so the amount of milk and water with him will be : 72 and 28 respectively.
7. In a  and  are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a 
and the area of a  is:
A    1:4
B    1:2
C    2:3
D    4:5
A n s w e r : A
Explanation:
We are given :
5
1
t h
? A B C, D, E F ? D E F
? A B C
  
.
Now In triangle ABC 
using the mid point theorem 
we get DE || BC and DE = 
Now ADE is similar to ABC 
So Area of ADE : Area of ABC = (DE/BC)^2 = 1:4 
Similarly Area of BDF :Area of ABC = 1:4
and Area of CEF : Area of ABC = 1:4 
Now we can say if area of ABC = 4A 
then area of ADE = area of BFD = area of CEF = a 
Therefore area of DEF = 4a-3a =a
so area of DEF : area of ABC = 1:4
    
8. A 100-meter long train crosses a 200-meter long and 20-meter wide bridge in 20 seconds. What is the speed of the train in
Km/hour?
A    45
B    36
C    54
D    57.6
A n s w e r : C
Explanation:
We will only consider length of bridge 
Now total distance = 100+200 = 300m
Now time taken to cross = 20 seconds 
Therefore speed = 15m/sec = 15(18/5) = 54km/hr
9. Given below are two statements:
Statement I: 
Statement II: If , then 
In light of the above statements, choose the correct answer from the options given below
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement I is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : D
Explanation:
From statement 1 we get 
Adding taking LCM 
= 12
So statement 1 is false 
Now statement 2 is an identity 
so 2 is true .
B C 2
1
( )
+ - 7 5
+ 7 5
= + 7 5
- 7 5
2
a + b + c = 0 ( a +
3
b +
3
c ) ÷
3
a b c = 3
7-5
+ + - (
 7 5
)
2
(
 7 5
)
2
  
.
Page 5


CMAT 2021 Slot-1
Quantitative Techniques and Data Interpretation
1. Two pipes A and B can fill a tank in 5 hours and 20 hours respectively. Both pipes together can fill the same tank in:
A    4 hours
B    6 hours
C    10 hours
D    2 hours
A n s w e r : A
Explanation:
Let the volume be 20 units 
So A fills at 4 units/hr 
B fills at 1 unit/hr
Now together they fill 4+1 = 5 units/ hour
Now time taken to fill completely : 20/5 = 4 hrs
2. In June-2020, the ratio of boys to girls in a college was 3 : 2. In September-2020, there were 80 fewer boys and 20 fewer girls in
the college and the ratio of boys to girls was 7 : 5. What was the total number of students in the college in June-2020?
A    1000
B    1100
C    1200
D    1300
A n s w e r : D
Explanation:
In June 2020 
Let the number of boys be 3x 
So number of girls will be 2x
Now number of boys in September 2020: 3x-80 and girls in September 2020 : 2x-20
Now as per given 3x-80:2x-20 =7:5
we get 15x-400 =14x-140
we get x=260
So number of students in June 2020 = 3x+2x =5x = 1300
3. M is a 4-digit number. If the left most digit is removed, then the resulting three digit number is  of M. How many such M's are
possible?
A    10
B    9
C    8
D    7
A n s w e r : D
Explanation:
According to question,
9
1
t h
  
.
Number AXYZ/9 = XYZ
It can be written as
A000/9 + XYZ/9 = XYZ
A000/9 + XYZ/9 = 9XYZ/9
A000/9 = 8XYZ/9
A000 = 8XYZ
We have to find the maximum value of A so that when A000 is divided by 8 gives three digit numbers.
7000/8= 875 and 8000/8=1000.
So, answer is 7.
4. L and M together can complete a piece of work in 72 days, M and N together can complete it in 120 days, and L and N together
in 90 days. In what time can L alone complete the work?
A    150 days
B    80 days
C    100 days
D    120 days
A n s w e r : D
Explanation:
Let L does a units of work/day 
M does b units of work/ day 
N does c units of work/ day 
Now as per given conditions :
Let work be W 
So we get 
W = 72(a+b) =120(b+c) =90(a+c)
we get 
6a+6b = 10b +10c 
we get 6a-4b-10c=0   (1)
also 
4a+4b =5a+5c
we get a-4b+5c =0   (2)
From (1) and (2) 
we get a=3 , b=2 and c=1 
Now therefore W = 360
Now time taken by L alone to complete the work = 360/3 = 120 days
5. Given below are two statements
Statement I : The set of numbers(5,6, 7, p, 6, 7, 8, q) has an arithmetic mean of 6 and mode (most frequently occurring number)
of 7. Then .
Statement II: Let p and q be two positive integers such that . Then .
In light of the above statements, choose the correct answer from the options given below
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement I is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : B
p × q = 16
p + q + p × q = 94 p + q = 20
  
.
Explanation:
we get 39+p+q =48
so p+q =9 
Now pq cannot be 16 for any value of p and q so 1 is false 
p+q+pq=94
we get p+q+pq+1 =95
we get (p+1)(q+1) =95
we get (0,94) ; (4,18)
So p+q is not 20 
Hence statement 2 is false
6. A milkman adds 10 litres of water to 90 litres of milk. After selling  of the total quantity, he adds water equal to the quantity
he sold. The proportion of water to milk he sells now would be:
A    72 : 28
B    28 : 72
C    20 : 80
D    30 : 70
A n s w e r : B
Explanation:
Initially Milkman has 90 liters of milk
Now amount of water added = 10 liters 
So total quantity becomes : 100 liters 
He sold 1/5 of quantity 
so he sold 2 liters of water and 18 liters of milk (A total of 20 liters is sold )
Now he is left with 10-2 = 8 liters of water  and 90-18 = 72 liters of milk.
Now he adds 20 liters of water 
so the amount of milk and water with him will be : 72 and 28 respectively.
7. In a  and  are the mid-points of the sides AB, BC and CA respectively. Then the ratio of the area of a 
and the area of a  is:
A    1:4
B    1:2
C    2:3
D    4:5
A n s w e r : A
Explanation:
We are given :
5
1
t h
? A B C, D, E F ? D E F
? A B C
  
.
Now In triangle ABC 
using the mid point theorem 
we get DE || BC and DE = 
Now ADE is similar to ABC 
So Area of ADE : Area of ABC = (DE/BC)^2 = 1:4 
Similarly Area of BDF :Area of ABC = 1:4
and Area of CEF : Area of ABC = 1:4 
Now we can say if area of ABC = 4A 
then area of ADE = area of BFD = area of CEF = a 
Therefore area of DEF = 4a-3a =a
so area of DEF : area of ABC = 1:4
    
8. A 100-meter long train crosses a 200-meter long and 20-meter wide bridge in 20 seconds. What is the speed of the train in
Km/hour?
A    45
B    36
C    54
D    57.6
A n s w e r : C
Explanation:
We will only consider length of bridge 
Now total distance = 100+200 = 300m
Now time taken to cross = 20 seconds 
Therefore speed = 15m/sec = 15(18/5) = 54km/hr
9. Given below are two statements:
Statement I: 
Statement II: If , then 
In light of the above statements, choose the correct answer from the options given below
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement I is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : D
Explanation:
From statement 1 we get 
Adding taking LCM 
= 12
So statement 1 is false 
Now statement 2 is an identity 
so 2 is true .
B C 2
1
( )
+ - 7 5
+ 7 5
= + 7 5
- 7 5
2
a + b + c = 0 ( a +
3
b +
3
c ) ÷
3
a b c = 3
7-5
+ + - (
 7 5
)
2
(
 7 5
)
2
  
.
10. Given below are two statements:
Statement I : Acoin is tossed three times. The probability of getting exactly two heads is 3/8
Statement II: In tossing of 10 coins, the probability of getting exactly 5 heads is 63/256
In the light of the above statements, choose the correct answer from the options given below.
A    Both Statement I and Statement II are true
B    Both Statement I and Statement II are false
C    Statement is true but Statement II is false
D    Statement I is false but Statement II is true
A n s w e r : A
Explanation:
Statement I:
Probability of getting head = P(H) = 
Probability of getting tail = P(T) = 
3 coins are tossed and probability of getting 2 heads =  = 
Statement I is true.
Statement II:
10 coins are tossed and probability of getting exactly 5 heads =  = 
Statement II is true
Answer is option A.
     
11. If  is a factor of , then (p,q) =
A    (5,2)
B    (5,4)
C    (-5,-4)
D    (-5,4)
A n s w e r : B
Explanation:
We have :
Now  is a factor of f(x) 
so we can say f(2) = f(1) =0 
substituting we get 
1-p+q =0 
p-q =1  
and 16-4p+q =0
4p-q =16
solving we get
p=5 and q =4
12. In a 100 meter race, A beats B by 10 meters and B beats C by 5 meters. By how many meters does A beat C?
2
1
2
1
3 C2 ( 2
1
)
2
( 2
1
) 8
3
10 C5 ( 2
1
)
5
( 2
1
)
5
256
63
x -
2
3 x + 2 x -
4
p x +
2
q
f x = ( ) x -
4
p x +
2
q
x -
2
3 x + 2 = x - 2 x - 1 ( ) ( )
  
.