IPMAT 2020: Past Year Question Paper with Answer Key | IPMAT Mock Test Series - Commerce PDF Download

 Page 1


IPMAT INDORE 2020
(Answers are at the bottom)
Quantitative Ability Short Answers:
1. In a division problem, the product of the quotient and the remainder is 24 while
their sum is 10. If the divisor is 5 then the dividend is __________.
2. The shortest distance from the point (-4, 3) to the circle x
2
+ y
2
= 1 is __________
3. The value of 0.04
( + + )
is ______________
?? ?? ?? 5
1
4
1
8
1
16
4. Suppose where a, b, and c are distinct real numbers. If a
= 3, then the value of abc is?
5. The minimum value of f(x) = |3 - x| + |2 + x| + |5 - x| is equal to __________
6. Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid
Rs. 86 to the shopkeeper. During his second visit, he purchased pens and
pencils in the ratio 4: 1 and paid Rs. 112 . The cost of a pen as well as a pencil in
rupees is a positive integer. If Ashok purchased four pens during his second visit,
then the amount he paid in rupees for the pens during the second visit is
__________.
7. In a four-digit number, the product of thousands digit and units digit is zero while
their difference is 7. Product of the middle digits is 18. The thousands digit is as
much more than the units digit as the hundreds digit is more than the tens digit.
The four-digit number is __________.
8. Out of 80 students who appeared for the school exams in Mathematics (M),
Physics (P) and Chemistry (C), 50 passed M , 30 passed P and 40 passed C. At
most 20 students passed M and P at most 20 students passed P and C and at
Page 2


IPMAT INDORE 2020
(Answers are at the bottom)
Quantitative Ability Short Answers:
1. In a division problem, the product of the quotient and the remainder is 24 while
their sum is 10. If the divisor is 5 then the dividend is __________.
2. The shortest distance from the point (-4, 3) to the circle x
2
+ y
2
= 1 is __________
3. The value of 0.04
( + + )
is ______________
?? ?? ?? 5
1
4
1
8
1
16
4. Suppose where a, b, and c are distinct real numbers. If a
= 3, then the value of abc is?
5. The minimum value of f(x) = |3 - x| + |2 + x| + |5 - x| is equal to __________
6. Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid
Rs. 86 to the shopkeeper. During his second visit, he purchased pens and
pencils in the ratio 4: 1 and paid Rs. 112 . The cost of a pen as well as a pencil in
rupees is a positive integer. If Ashok purchased four pens during his second visit,
then the amount he paid in rupees for the pens during the second visit is
__________.
7. In a four-digit number, the product of thousands digit and units digit is zero while
their difference is 7. Product of the middle digits is 18. The thousands digit is as
much more than the units digit as the hundreds digit is more than the tens digit.
The four-digit number is __________.
8. Out of 80 students who appeared for the school exams in Mathematics (M),
Physics (P) and Chemistry (C), 50 passed M , 30 passed P and 40 passed C. At
most 20 students passed M and P at most 20 students passed P and C and at
most 20 students passed C and M. The maximum number of students who could
have passed all three exams is __________.
9. Two friends run a 3-kilometer race along a circular course of length 300 meters. If
their speeds are in the ratio 3:2, the number of times the winner passes the other
is __________.
10.Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of
ways we can choose 4 objects out of 13 objects is __________.
Quantitative Ability and Data Interpretation - Multiple Choice
11. The probability that a randomly chosen factor of 10
19
is a multiple of 10
15
is
A.
1
25
B.
1
12
C.
1
20
D.
1
16
12.The number of acute angled triangles whose sides are three consecutive positive
integers and whose perimeter is at most 100 is
A. 28
B. 29
C. 31
D. 33
13.The equation of the straight line passing through the point M (-5,1), such that the
portion of it between the axes is divided by the point M in to two equal halves, is
A. 10y - 8x = 80
B. 8y + 10x = 80
C. 10y + 8x = 80
D. 8y + 10x + 80 = 0
14.The value of cos
2
+ cos
2
+ cos
2
+ cos
2
p
8
3p
8
5p
8
7p
8
A. 1
B.
3
2
Page 3


IPMAT INDORE 2020
(Answers are at the bottom)
Quantitative Ability Short Answers:
1. In a division problem, the product of the quotient and the remainder is 24 while
their sum is 10. If the divisor is 5 then the dividend is __________.
2. The shortest distance from the point (-4, 3) to the circle x
2
+ y
2
= 1 is __________
3. The value of 0.04
( + + )
is ______________
?? ?? ?? 5
1
4
1
8
1
16
4. Suppose where a, b, and c are distinct real numbers. If a
= 3, then the value of abc is?
5. The minimum value of f(x) = |3 - x| + |2 + x| + |5 - x| is equal to __________
6. Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid
Rs. 86 to the shopkeeper. During his second visit, he purchased pens and
pencils in the ratio 4: 1 and paid Rs. 112 . The cost of a pen as well as a pencil in
rupees is a positive integer. If Ashok purchased four pens during his second visit,
then the amount he paid in rupees for the pens during the second visit is
__________.
7. In a four-digit number, the product of thousands digit and units digit is zero while
their difference is 7. Product of the middle digits is 18. The thousands digit is as
much more than the units digit as the hundreds digit is more than the tens digit.
The four-digit number is __________.
8. Out of 80 students who appeared for the school exams in Mathematics (M),
Physics (P) and Chemistry (C), 50 passed M , 30 passed P and 40 passed C. At
most 20 students passed M and P at most 20 students passed P and C and at
most 20 students passed C and M. The maximum number of students who could
have passed all three exams is __________.
9. Two friends run a 3-kilometer race along a circular course of length 300 meters. If
their speeds are in the ratio 3:2, the number of times the winner passes the other
is __________.
10.Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of
ways we can choose 4 objects out of 13 objects is __________.
Quantitative Ability and Data Interpretation - Multiple Choice
11. The probability that a randomly chosen factor of 10
19
is a multiple of 10
15
is
A.
1
25
B.
1
12
C.
1
20
D.
1
16
12.The number of acute angled triangles whose sides are three consecutive positive
integers and whose perimeter is at most 100 is
A. 28
B. 29
C. 31
D. 33
13.The equation of the straight line passing through the point M (-5,1), such that the
portion of it between the axes is divided by the point M in to two equal halves, is
A. 10y - 8x = 80
B. 8y + 10x = 80
C. 10y + 8x = 80
D. 8y + 10x + 80 = 0
14.The value of cos
2
+ cos
2
+ cos
2
+ cos
2
p
8
3p
8
5p
8
7p
8
A. 1
B.
3
2
C. 2
D.
9
4
15.If + + + upto = , then the value of + + + …… upto
1
1
2
1
2
2
1
3
2
8 
p
2
6
1
1
2
1
3
2
1
5
2
8 
is
A.
p
2
8
B.
p
2
16
C.
p
2
12
D.
p
2
36
16.A man is known to speak the truth on an average 4 out of 5 times. He throws a
die and reports that it is a five. The probability that it is actually a five is
A.
4
9
B.
5
9
C.
4
15
D.
2
15
17.If log
5
log
8
(x2 - 1) = 0, then a possible value of x is
A. 2 2
B. 2
C. 2
D. 3
18.Consider the following statements:
(i) When  0 < x < 1, then < 1 - x + x
2
1
1+?? (ii) When  0 < x < 1, then > 1 - x + x
2
1
1+?? (iii) When  -1 < x < 0, then < 1 - x + x
2
1
1+?? (iv) When  -1 < x < 0, then > 1 - x + x
2
1
1+??
Page 4


IPMAT INDORE 2020
(Answers are at the bottom)
Quantitative Ability Short Answers:
1. In a division problem, the product of the quotient and the remainder is 24 while
their sum is 10. If the divisor is 5 then the dividend is __________.
2. The shortest distance from the point (-4, 3) to the circle x
2
+ y
2
= 1 is __________
3. The value of 0.04
( + + )
is ______________
?? ?? ?? 5
1
4
1
8
1
16
4. Suppose where a, b, and c are distinct real numbers. If a
= 3, then the value of abc is?
5. The minimum value of f(x) = |3 - x| + |2 + x| + |5 - x| is equal to __________
6. Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid
Rs. 86 to the shopkeeper. During his second visit, he purchased pens and
pencils in the ratio 4: 1 and paid Rs. 112 . The cost of a pen as well as a pencil in
rupees is a positive integer. If Ashok purchased four pens during his second visit,
then the amount he paid in rupees for the pens during the second visit is
__________.
7. In a four-digit number, the product of thousands digit and units digit is zero while
their difference is 7. Product of the middle digits is 18. The thousands digit is as
much more than the units digit as the hundreds digit is more than the tens digit.
The four-digit number is __________.
8. Out of 80 students who appeared for the school exams in Mathematics (M),
Physics (P) and Chemistry (C), 50 passed M , 30 passed P and 40 passed C. At
most 20 students passed M and P at most 20 students passed P and C and at
most 20 students passed C and M. The maximum number of students who could
have passed all three exams is __________.
9. Two friends run a 3-kilometer race along a circular course of length 300 meters. If
their speeds are in the ratio 3:2, the number of times the winner passes the other
is __________.
10.Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of
ways we can choose 4 objects out of 13 objects is __________.
Quantitative Ability and Data Interpretation - Multiple Choice
11. The probability that a randomly chosen factor of 10
19
is a multiple of 10
15
is
A.
1
25
B.
1
12
C.
1
20
D.
1
16
12.The number of acute angled triangles whose sides are three consecutive positive
integers and whose perimeter is at most 100 is
A. 28
B. 29
C. 31
D. 33
13.The equation of the straight line passing through the point M (-5,1), such that the
portion of it between the axes is divided by the point M in to two equal halves, is
A. 10y - 8x = 80
B. 8y + 10x = 80
C. 10y + 8x = 80
D. 8y + 10x + 80 = 0
14.The value of cos
2
+ cos
2
+ cos
2
+ cos
2
p
8
3p
8
5p
8
7p
8
A. 1
B.
3
2
C. 2
D.
9
4
15.If + + + upto = , then the value of + + + …… upto
1
1
2
1
2
2
1
3
2
8 
p
2
6
1
1
2
1
3
2
1
5
2
8 
is
A.
p
2
8
B.
p
2
16
C.
p
2
12
D.
p
2
36
16.A man is known to speak the truth on an average 4 out of 5 times. He throws a
die and reports that it is a five. The probability that it is actually a five is
A.
4
9
B.
5
9
C.
4
15
D.
2
15
17.If log
5
log
8
(x2 - 1) = 0, then a possible value of x is
A. 2 2
B. 2
C. 2
D. 3
18.Consider the following statements:
(i) When  0 < x < 1, then < 1 - x + x
2
1
1+?? (ii) When  0 < x < 1, then > 1 - x + x
2
1
1+?? (iii) When  -1 < x < 0, then < 1 - x + x
2
1
1+?? (iv) When  -1 < x < 0, then > 1 - x + x
2
1
1+?? Then the correct statements are
A. (i) and (ii)
B. (ii) and (iv)
C. (i) and (iv)
D. (ii) and (iii)
19.Fifty litres of a mixture of milk and water contains 30 percent of water. This
mixture is added to eighty litres of another mixture of milk and water that contains
20 percent of water. Then, how many litres of water should be added to the
resulting mixture to obtain a final mixture that contains 25 percent of water?
A. 1
B. 2
C. 3
D. 4
20.Three workers working together need 1 hour to construct a wall. The first worker,
working alone, can construct the wall twice as fast at the third worker, and can
complete the task an hour sooner than the second worker. Then, the average
time in hours taken by the three workers, when working alone, to construct the
wall is
A.
33 + 4
3
B.
33 + 5
3
C.
33 + 6
3
D.
33 + 7
3
21.In a class, students are assigned roll numbers from 1 to 140. All students with
even roll numbers opted for cricket, all those whose roll numbers are divisible by
5 opted for football, and all those whose roll numbers are divisible by 3 opted for
basketball. 'The number of students who did not opt for any of the three sports is
A. 102
B. 38
C. 98
D. 42
22.Given f(x) = x
2
+ log
3
x and g(y) = 2y + f(y), then the value of g(3) equals
A. 16
B. 15
C. 25
Page 5


IPMAT INDORE 2020
(Answers are at the bottom)
Quantitative Ability Short Answers:
1. In a division problem, the product of the quotient and the remainder is 24 while
their sum is 10. If the divisor is 5 then the dividend is __________.
2. The shortest distance from the point (-4, 3) to the circle x
2
+ y
2
= 1 is __________
3. The value of 0.04
( + + )
is ______________
?? ?? ?? 5
1
4
1
8
1
16
4. Suppose where a, b, and c are distinct real numbers. If a
= 3, then the value of abc is?
5. The minimum value of f(x) = |3 - x| + |2 + x| + |5 - x| is equal to __________
6. Ashok purchased pens and pencils in the ratio 2: 3 during his first visit and paid
Rs. 86 to the shopkeeper. During his second visit, he purchased pens and
pencils in the ratio 4: 1 and paid Rs. 112 . The cost of a pen as well as a pencil in
rupees is a positive integer. If Ashok purchased four pens during his second visit,
then the amount he paid in rupees for the pens during the second visit is
__________.
7. In a four-digit number, the product of thousands digit and units digit is zero while
their difference is 7. Product of the middle digits is 18. The thousands digit is as
much more than the units digit as the hundreds digit is more than the tens digit.
The four-digit number is __________.
8. Out of 80 students who appeared for the school exams in Mathematics (M),
Physics (P) and Chemistry (C), 50 passed M , 30 passed P and 40 passed C. At
most 20 students passed M and P at most 20 students passed P and C and at
most 20 students passed C and M. The maximum number of students who could
have passed all three exams is __________.
9. Two friends run a 3-kilometer race along a circular course of length 300 meters. If
their speeds are in the ratio 3:2, the number of times the winner passes the other
is __________.
10.Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of
ways we can choose 4 objects out of 13 objects is __________.
Quantitative Ability and Data Interpretation - Multiple Choice
11. The probability that a randomly chosen factor of 10
19
is a multiple of 10
15
is
A.
1
25
B.
1
12
C.
1
20
D.
1
16
12.The number of acute angled triangles whose sides are three consecutive positive
integers and whose perimeter is at most 100 is
A. 28
B. 29
C. 31
D. 33
13.The equation of the straight line passing through the point M (-5,1), such that the
portion of it between the axes is divided by the point M in to two equal halves, is
A. 10y - 8x = 80
B. 8y + 10x = 80
C. 10y + 8x = 80
D. 8y + 10x + 80 = 0
14.The value of cos
2
+ cos
2
+ cos
2
+ cos
2
p
8
3p
8
5p
8
7p
8
A. 1
B.
3
2
C. 2
D.
9
4
15.If + + + upto = , then the value of + + + …… upto
1
1
2
1
2
2
1
3
2
8 
p
2
6
1
1
2
1
3
2
1
5
2
8 
is
A.
p
2
8
B.
p
2
16
C.
p
2
12
D.
p
2
36
16.A man is known to speak the truth on an average 4 out of 5 times. He throws a
die and reports that it is a five. The probability that it is actually a five is
A.
4
9
B.
5
9
C.
4
15
D.
2
15
17.If log
5
log
8
(x2 - 1) = 0, then a possible value of x is
A. 2 2
B. 2
C. 2
D. 3
18.Consider the following statements:
(i) When  0 < x < 1, then < 1 - x + x
2
1
1+?? (ii) When  0 < x < 1, then > 1 - x + x
2
1
1+?? (iii) When  -1 < x < 0, then < 1 - x + x
2
1
1+?? (iv) When  -1 < x < 0, then > 1 - x + x
2
1
1+?? Then the correct statements are
A. (i) and (ii)
B. (ii) and (iv)
C. (i) and (iv)
D. (ii) and (iii)
19.Fifty litres of a mixture of milk and water contains 30 percent of water. This
mixture is added to eighty litres of another mixture of milk and water that contains
20 percent of water. Then, how many litres of water should be added to the
resulting mixture to obtain a final mixture that contains 25 percent of water?
A. 1
B. 2
C. 3
D. 4
20.Three workers working together need 1 hour to construct a wall. The first worker,
working alone, can construct the wall twice as fast at the third worker, and can
complete the task an hour sooner than the second worker. Then, the average
time in hours taken by the three workers, when working alone, to construct the
wall is
A.
33 + 4
3
B.
33 + 5
3
C.
33 + 6
3
D.
33 + 7
3
21.In a class, students are assigned roll numbers from 1 to 140. All students with
even roll numbers opted for cricket, all those whose roll numbers are divisible by
5 opted for football, and all those whose roll numbers are divisible by 3 opted for
basketball. 'The number of students who did not opt for any of the three sports is
A. 102
B. 38
C. 98
D. 42
22.Given f(x) = x
2
+ log
3
x and g(y) = 2y + f(y), then the value of g(3) equals
A. 16
B. 15
C. 25
D. 26
23.A 2 × 2 matrix is filled with four distinct integers randomly chosen from the set
{1,2,3,4,5,6}. Then the probability that the matrix generated in such a way is
singular is
A.
2
45
B.
1
45
C.
4
15
D.
1
15
24.Ashok started a business with a certain investment. After a few months, Bharat
joined him, investing half the amount of Ashok's initial investment. At the end of
the first year, the total profit was divided between them in ratio 3:1 . Bharat joined
Ashok after
A. 2 months
B. 3 months
C. 4 months
D. 6 months
25.The average marks of 6 students in a test is 64 . All the students got different
marks, one of the students obtained 70 marks and all other students scored 40 or
above. The maximum possible difference between the second highest and the
second lowest marks is
A. 50
B. 54
C. 57
D. 58