IPMAT Indore 2024 Quantitative Aptitude: All Questions with Video & Short Solutions
- Anshu Agarwal
- Aug 2
- 10 min read
Updated: Aug 7
Preparing for IPMAT 2025 or IPMAT 2026? The best way to improve is by analysing previous year’s actual questions. In this blog, you will find all the Quantitative Aptitude (QA) questions from IPMAT 2024 (conducted by IIM Indore), with detailed video solutions by Anshu Sir, and wherever applicable, a short trick or shortcut-based solution as well.
This is not just a blog post — this is your free, one-stop solution bank to understand what IPMAT truly tests and how toppers approach each question!
📘 IPMAT Indore 2024 Quantitative Aptitude Question-wise Solutions:
[A] Short Answers:
1. Let ABC be a triangle right–angled at B with AB = BC = 18. The area of largest rectangle that can be inscribed in this triangle and has B as one of the vertices is:
2. If 4ˡᵒᵍ₂ˣ − 4x + 9ˡᵒᵍ₃ʸ − 16y + 68 = 0 , then y − x equals:
3. A fruit seller has oranges, apples and bananas in the ratio 3: 6: 7. If the number of
oranges is a multiple of both 5 and 6, then minimum number of fruits the seller has is :
4. The number of triangles with integer sides and with perimeter 15 is:
5. The number of real solutions of the equation
(x² − 15x + 55)ˣ²⁻⁵ˣ⁺⁶ = 1 is:
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6. In a group of 150 students, 52 like tea, 48 like juice, and 62 like coffee. If each student in the group likes at least one among the tea, juice, and coffee, then the maximum number of students that like more than one drink is:
Directions [7 – 9]:
The following table shows the number of employees and their median age in eight companies located in a district:
Company | Number of Employees | Median Age |
A | 32 | 24 |
B | 28 | 30 |
C | 43 | 39 |
D | 39 | 45 |
E | 35 | 49 |
F | 29 | 54 |
G | 23 | 59 |
H | 16 | 63 |
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B. The age of every employee in B is strictly less than the age of every employee in C,… The age of every employee in G is strictly less than the age of every employee in H.
7. The median age of employees across the eight companies is:
8. The highest possible age of an employee of company A is:
9. In company F, the lowest possible sum of the ages of all employees is:
Short Explanation:
10. The number of pairs (x, y) of integers satisfying the inequality
|x − 5| + |y − 5| ≤ 6 is:
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11. The price of chocolate is increased by x% and then reduced by x%. The new price is 96.76% of the original price, then x is:
12. Let f and g be two functions defined by
f(x) = |(x + |x|) and g(x) = 1/x for x ≠ 0.
If f(a) + g(f(a)) = 13/6 for some real a, then the maximum possible value of f(g(a)) is:
13. If
is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is:
14. The number of factors of 1800 that are multiples of 6 is:
15. Person A borrows ₹4000 from another person B for a duration of 4 years. He borrows a portion of it at 3% simple interest per annum while the rest at 4% simple interest per annum. If he gets ₹520 as total interest, then the amount A borrowed at 3% per annum is (in rupees):
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[B] MCQ :
1. If θ is the angle between the pair of tangents drawn from the point A(0, 7/2) to the circle
x² + y² − 14x + 16y + 88 = 0,
then tan θ equals:
(a) 4/5
(b) 5/4
(c) 20/21
(d) 2/5
Short Explanation:
2. The side AB of a triangle ABC is c. The median BD is of length k. If ∠BDA = θ < 90°, then the area of triangle ABCis:
(a) (k² cos 2θ)⁄2 + k sin θ √(c² − k² cos² θ)
(b) (k² cos θ)⁄4 − k sin θ √(c² + k² sin² θ)
(c) (k² sin θ)⁄4 + k sin θ √(c² − k² sin² θ)
(d) (k² sin 2θ)⁄2 + k sin θ √(c² − k² sin² θ)
3. If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle is:
(a) 2.5 cm
(b) 6.5 cm
(c) 5 cm or 13 cm
(d) 2.5 cm or 6.5 cm
4. Let ABC be a triangle with AB = AC and D be a point on BC such that ∠BAD = 30°. If E is a point on AC such that AD = AE, then ∠CDE equals:
(a) 15°
(b) 10°
(c) 30°
(d) 60°
5. Let ABC be an equilateral triangle, with each side of length k. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is:
(a) (3√3 + π)·(k²⁄24)
(b) (3√3 − π)·(k²⁄24)
(c) (3√3 + π)·(k²⁄6)
(d) (3√3 − π)·(k²⁄6)
Short Explanation:
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6. The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle of elevation changes to 45°, after moving 20 meters towards the base of the pole. Then the height of the pole, in meters, is:
(a) 10(√3 + 1)
(b) 15(√5 + 1)
(c) 20(√3 + 1)
(d) 30
Short Explanation:
7. The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is:
(a) 200
(b) 27
(c) 25
(d) 100
8. Let a = (log₇4 × (log₇5 − log₇2)) ÷ (log₇25 × (log₇8 − log₇4))
Find the value of 5ᵃ:
(a) 5⁄2
(b) 5
(c) 7⁄2
(d) 8
9. The numbers 2²⁰²⁴ and 5²⁰²⁴ are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is:
(a) 1987
(b) 2065
(c) 2000
(d) 2025
10. If log₄x = a and log₂₅x = b, then logₓ10 is:
(a) (a + b)/2
(b) (a − b)/(2ab)
(c) (a + b)/(2ab)
(d) (a + b)/[2(a − b)]
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11. The number of solutions of the equation
x₁ + x₂ + x₃ + x₄ = 50,
where x₁ ≥ 1, x₂ ≥ 2, x₃ ≥ 0, x₄ ≥ 0, is:
(a) 20200
(b) 19600
(c) 19200
(d) 18400
12. A fruit seller had a certain number of apples, bananas, and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of the apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was
(a) 190
(b) 210
(c) 220
(d) 180
Short Explanation:
13. The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of n for which the sum of its first n terms is closest to 100, is:
(a) 5
(b) 4
(c) 6
(d) 7
Short Explanation:
14. The greatest number among the following is: 2³⁰⁰, 3²⁰⁰, 4¹⁰⁰, 2¹⁰⁰ + 3¹⁰⁰
(a) 2³⁰⁰
(b) 3²⁰⁰
(c) 4¹⁰⁰
(d) 2¹⁰⁰ + 3¹⁰⁰
15. For some non-zero real values of a, b and c, it is given that:
|c/a| = 4
|a/b| = 1/3
b/c = –3/4
ac > 0
Then the value of (b + c)/a is:
(a) –1
(b) 1
(c) 7
(d) –7
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16. The terms of a geometric progression are real and positive. If the p-th term of the progression is q and the q-th term is p, then the logarithm of the first term is:
(a) [(1 - q) log(p) - (1 - p) log(q)] / (p - q)
(b) [(1 - q) log(q) + (1 - p) log(p)] / (p - q)
(c) [(1 - q) log(q) - (1 - p) log(p)] / (p - q)
(d) [(1 - q) log(p) + (1 - p) log(q)] / (p - q)
Short Explanation:
17. A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day, the boat starts from point A, goes downstream for 1 hour, then upstream for 1 hour, and repeats this for 4 more times (total 5 upstream and 5 downstream journeys). Then the boat would be:
(a) 15 km downstream of A
(b) 22.5 km downstream of A
(c) 20 km downstream of A
(d) 12.5 km downstream of A
18. The difference between the maximum real root and the minimum real root of the equation:
(x² – 5)⁴ + (x² – 7)⁴ = 16 is:
(a) 2√7
(b) √7
(c) √10
(d) 2√5
If |x + 1| + (y + 2)² = 0 and a·x – 3a·y = 1
then the value of a is:
(a) 2
(b) 1/5
(c) 1/2
(d) 1/7
20. Let n be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then
(a) 6000 ≤ n < 7000
(b) 9000 ≤ n < 10000
(c) 7000 ≤ n < 8000
(d) 8000 ≤ n < 9000
Short Explanation:
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21. If 5 boys and 3 girls randomly sit around a circular table, the probability that there will be at least one boy sitting between any two girls is:
(a) 1/4
(b) 1/3
(c) 1/7
(d) 2/7
22. Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is :
(a) 1111
(b) 1000
(c) 1130
(d) 1100
Short Explanation:
23. The number of values of x for which C(17 − x, 3x + 1) is defined as an integer:
(a) 5
(b) 2
(c) 4
(d) 8
24. The number of real solutions of the equation
x² − 10|x| − 56 = 0 is:
(a) 3
(b) 1
(c) 2
(d) 4
25. In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is :
(a) 60
(b) 100
(c) 75
(d) 50
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Directions [26 – 30]:
In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each all of whom voted. Three parties A, B and C contested the elections.
The party that gets maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available :
• Total number of votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively.
• S2 and S3 were won by C while A won only S1.
• Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.
26. The number of votes obtained by B in S2 is:
(a) 7
(b) 4
(c) 5
(d) 6
27. The constituency in which B got lower number of votes compared to A and C is
(a) S1
(b) S2
(c) S4
(d) S3
28. The number of votes obtained by A in S5 is
(a) 9
(b) 7
(c) 6
(d) 8
29. Comparing the number votes obtained by A across different constituencies, the lowest number of votes were in constituency
(a) S5
(b) S2
(c) S4
(d) S3
30. Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is
(a) 3
(b) 5
(c) 4
(d) 2
Short Explanation:
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