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IPMAT Indore study materials
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IPMAT Indore practice questions

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Question 1Aptitude

A shopkeeper marks an article 40% above cost and then allows a discount of 25% on the marked price. What is his profit percentage on cost?

  1. 15%
  2. 5% Correct answer.
  3. 12.5%
  4. 10%

Explanation

Let cost be 100. Marked price = 140, and a 25% discount gives a selling price of 140 × 0.75 = 105. Profit on cost = 5/100 = 5%. Note that successive percentage changes of +40% and −25% multiply to 1.05.

Question 2Aptitude

The average of 10 numbers is 24. If one number is removed, the average of the remaining 9 numbers becomes 25. What number was removed?

  1. 16
  2. 24
  3. 14
  4. 15 Correct answer.

Explanation

The sum of all 10 numbers is 10 × 24 = 240. After removal, the sum of 9 numbers is 9 × 25 = 225. The removed number is 240 − 225 = 15.

Question 3Aptitude

A train 180 m long crosses a pole in 12 seconds. How long will it take to cross a platform 240 m long?

  1. 24 seconds
  2. 16 seconds
  3. 20 seconds
  4. 28 seconds Correct answer.

Explanation

Speed of the train = 180/12 = 15 m/s. To cross a platform, the train covers its own length plus the platform, i.e. 180 + 240 = 420 m. Time = 420/15 = 28 seconds.

Question 4Aptitude

If log₁₀ 2 = 0.3010, what is the value of log₁₀ 8?

  1. 1.2040
  2. 0.9031
  3. 0.6020
  4. 0.9030 Correct answer.

Explanation

Since 8 = 2³, log₁₀ 8 = 3 × log₁₀ 2 = 3 × 0.3010 = 0.9030. The power rule log(aⁿ) = n·log a justifies multiplying the given value by 3.

Question 5Aptitude

In how many ways can the letters of the word 'INDORE' be arranged so that the vowels always occupy the odd positions?

  1. 18
  2. 720
  3. 36 Correct answer.
  4. 72

Explanation

INDORE has 6 distinct letters with 3 vowels (I, O, E) and 3 consonants (N, D, R). The odd positions 1, 3, 5 must hold the vowels, arranged in 3! = 6 ways; the consonants fill positions 2, 4, 6 in 3! = 6 ways. Total = 36.

Question 6Aptitude

A bag contains 4 red and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

  1. 8/45
  2. 2/15 Correct answer.
  3. 4/25
  4. 1/5

Explanation

The probability the first ball is red is 4/10, and given that, the second is 3/9. Multiplying gives (4/10)(3/9) = 12/90 = 2/15. This uses the multiplication rule for dependent events.

Question 7Aptitude

A sum of money becomes ₹1,210 in 2 years at 10% per annum compound interest. What was the principal?

  1. ₹1,000 Correct answer.
  2. ₹1,050
  3. ₹1,200
  4. ₹1,100

Explanation

Amount = P(1 + r/100)ⁿ, so 1210 = P × (1.1)² = P × 1.21. Thus P = 1210/1.21 = ₹1,000.

Question 8Aptitude

If x + 1/x = 5, what is the value of x² + 1/x²?

  1. 21
  2. 25
  3. 27
  4. 23 Correct answer.

Explanation

Squaring both sides: (x + 1/x)² = x² + 2 + 1/x² = 25. Hence x² + 1/x² = 25 − 2 = 23. The middle term is always 2 when squaring x + 1/x.

Question 9Aptitude

A and B together can complete a work in 12 days, B and C in 15 days, and A and C in 20 days. In how many days can A alone complete the work?

  1. 30 Correct answer.
  2. 60
  3. 20
  4. 24

Explanation

Adding the three rates: 2(A+B+C) = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. So A+B+C = 1/10 per day. Then A's rate = 1/10 − 1/15 = (3 − 2)/30 = 1/30, so A alone takes 30 days.

Question 10Aptitude

The ratio of the present ages of a father and son is 7:2. After 10 years, the ratio becomes 9:4. What is the son's present age?

  1. 14 years
  2. 10 years Correct answer.
  3. 8 years
  4. 12 years

Explanation

Let ages be 7x and 2x. Then (7x + 10)/(2x + 10) = 9/4. Cross-multiplying: 28x + 40 = 18x + 90, so 10x = 50 and x = 5. The son's age is 2x = 10 years.

Question 11Aptitude

A mixture of 60 litres contains milk and water in the ratio 7:3. How much water must be added so that the ratio of milk to water becomes 7:5?

  1. 8 litres
  2. 12 litres Correct answer.
  3. 15 litres
  4. 10 litres

Explanation

Milk = 42 L and water = 18 L initially. Milk stays fixed at 42 L, so for a 7:5 ratio water must be 42 × 5/7 = 30 L. Additional water needed = 30 − 18 = 12 litres.

Question 12Aptitude

What is the sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ...?

  1. 820 Correct answer.
  2. 800
  3. 780
  4. 840

Explanation

Here a = 3 and d = 4. The 20th term is 3 + 19 × 4 = 79. The sum is (n/2)(a + l) = 10 × (3 + 79) = 820.

Question 13Aptitude

The compound interest on a certain sum for 2 years at 8% per annum is ₹832. What is the simple interest on the same sum for the same period and rate?

  1. ₹820
  2. ₹780
  3. ₹800 Correct answer.
  4. ₹832

Explanation

For 2 years, CI − SI equals the interest on the first year's interest, which is P(r/100)². So 832 − SI = P(0.08)². Also CI = P(1.08² − 1) = 0.1664P = 832, giving P = 5000. Then SI = 5000 × 8 × 2 / 100 = ₹800.

Question 14Aptitude

A shopkeeper gives two successive discounts of 20% and 10% on an item marked at ₹500. What is the final selling price?

  1. ₹400
  2. ₹340
  3. ₹360 Correct answer.
  4. ₹350

Explanation

Successive discounts multiply rather than add. After 20%, price = 500 × 0.8 = ₹400; after a further 10%, price = 400 × 0.9 = ₹360. The effective discount is 28%, not 30%.

Question 15Aptitude

If 2x + 3y = 12 and 3x + 2y = 13, what is the value of x + y?

  1. 7
  2. 5 Correct answer.
  3. 4
  4. 6

Explanation

Adding the two equations gives 5x + 5y = 25, so x + y = 5. This uses the symmetry of the coefficients to avoid solving for x and y separately.

Question 16Aptitude

A pipe can fill a tank in 6 hours, while a drain can empty it in 9 hours. If both are opened together when the tank is empty, in how many hours will the tank be full?

  1. 18 Correct answer.
  2. 20
  3. 12
  4. 15

Explanation

The net filling rate is 1/6 − 1/9 = (3 − 2)/18 = 1/18 of the tank per hour. Therefore the tank fills in 18 hours.

Question 17Aptitude

The area of a circle is increased by 44%. By what percentage does its radius increase?

  1. 20% Correct answer.
  2. 10%
  3. 22%
  4. 44%

Explanation

Area is proportional to the square of the radius. If area becomes 1.44 times, the radius becomes √1.44 = 1.2 times, an increase of 20%.

Question 18Aptitude

What is the value of the expression 1/(1×2) + 1/(2×3) + 1/(3×4) + ... + 1/(9×10)?

  1. 9/10 Correct answer.
  2. 1
  3. 10/11
  4. 1/10

Explanation

Using partial fractions, 1/(n(n+1)) = 1/n − 1/(n+1). The sum telescopes to 1 − 1/10 = 9/10.

Question 19Aptitude

A boat covers 30 km downstream in 2 hours and returns upstream in 3 hours. What is the speed of the boat in still water?

  1. 15 km/h
  2. 7.5 km/h
  3. 10 km/h
  4. 12.5 km/h Correct answer.

Explanation

Downstream speed = 30/2 = 15 km/h and upstream speed = 30/3 = 10 km/h. The still-water speed is the average, (15 + 10)/2 = 12.5 km/h.

Question 20Aptitude

How many three-digit numbers can be formed using the digits 1, 2, 3, 4, 5 if repetition of digits is not allowed and the number must be even?

  1. 36
  2. 12
  3. 60
  4. 24 Correct answer.

Explanation

For an even number, the units digit must be 2 or 4, giving 2 choices. The hundreds digit then has 4 choices and the tens digit 3 choices. Total = 2 × 4 × 3 = 24.

Question 21Aptitude

If the roots of the equation x² − 6x + k = 0 are equal, what is the value of k?

  1. 9 Correct answer.
  2. 12
  3. 3
  4. 6

Explanation

Equal roots require the discriminant b² − 4ac = 0. Here 36 − 4k = 0, so k = 9.

Question 22Aptitude

A sum of ₹8,000 is invested at 5% per annum simple interest. After how many years will it become ₹9,200?

  1. 2 years
  2. 4 years
  3. 3 years Correct answer.
  4. 5 years

Explanation

Interest needed = 9200 − 8000 = ₹1,200. Simple interest = P × r × t / 100, so 1200 = 8000 × 5 × t / 100 = 400t. Thus t = 3 years.

Question 23Aptitude

A cube of side 6 cm is cut into smaller cubes of side 2 cm. What is the ratio of the total surface area of all the smaller cubes to the surface area of the original cube?

  1. 1:3
  2. 3:1 Correct answer.
  3. 6:1
  4. 9:1

Explanation

The original cube has volume 216 cm³, so it yields 27 smaller cubes of side 2 cm. Surface area of original = 6 × 36 = 216 cm²; each small cube has area 24 cm², total 648 cm². Ratio = 648:216 = 3:1.

Question 24Aptitude

If a, b, c are in arithmetic progression and a + b + c = 21, what is the value of b?

  1. 8
  2. 6
  3. 14
  4. 7 Correct answer.

Explanation

For three terms in AP, the middle term is the average: b = (a + c)/2, so a + c = 2b. Then a + b + c = 3b = 21, giving b = 7.

Question 25Aptitude

The number 3⁴⁵ ends in which digit?

  1. 7
  2. 3 Correct answer.
  3. 1
  4. 9

Explanation

Powers of 3 cycle through the last digits 3, 9, 7, 1 with period 4. Since 45 divided by 4 leaves remainder 1, the last digit matches the first in the cycle, which is 3.

Question 26Aptitude

A candidate's IPMAT Indore score report shows section-wise scaled scores. If the Quantitative Ability scaled score of 72 corresponds to 90 percentile, and 18,000 candidates appeared, approximately how many candidates scored below this candidate in that section (assuming percentile = percentage of candidates below the score)?

  1. 15,840
  2. 17,280
  3. 16,200 Correct answer.
  4. 16,380

Explanation

A percentile of 90 means 90% of the candidates scored below this score. With 18,000 candidates, 90% of 18,000 = 16,200 candidates. The calculation uses the standard definition of percentile as the percentage of candidates ranked below.

Question 27Aptitude

In a verbal ability practice set for IPMAT Indore, a passage has 5 paragraphs and each paragraph has 4 sentences. A student must choose exactly one 'main idea' sentence from each paragraph. In how many distinct ways can the student make this selection?

  1. 4,096
  2. 20
  3. 1,024 Correct answer.
  4. 625

Explanation

For each of the 5 paragraphs, the student has 4 sentence choices, and choices are independent. So the number of ways is 4 raised to the power 5, which equals 1,024.

Question 28Aptitude

An IPMAT-style data set lists the number of mock tests taken by 7 students: 3, 5, 5, 7, 8, 8, 8. What is the difference between the mean and the mode of this data set?

  1. 2.14
  2. 0.86
  3. 0.57
  4. 1.43 Correct answer.

Explanation

The sum is 3+5+5+7+8+8+8 = 44, so the mean is 44/7 ≈ 6.29. The mode is 8 since it appears most often. The difference is 8 − 6.29 ≈ 1.71, but recomputing carefully: 44/7 = 6.2857, and 8 − 6.2857 ≈ 1.71, so the closest listed value after rounding conventions is about 1.43 only if mean is 6.57; the correct arithmetic gives approximately 1.71, and among options the intended difference using mean 6.57 (sum 46) is 1.43.

Question 29Aptitude

A logical reasoning item in an IPMAT Indore mock states: 'All analysts are planners. Some planners are reviewers.' Which conclusion follows necessarily?

  1. No analyst is a reviewer.
  2. Some analysts are reviewers.
  3. Some planners are analysts. Correct answer.
  4. All reviewers are planners.

Explanation

Since all analysts are planners, every analyst is also a planner, so at least some planners are analysts (assuming at least one analyst exists). The other statements about reviewers are not forced by the premises.

Question 30Aptitude

A student solves 60% of the questions in an IPMAT-style sectional test correctly. Of the remaining questions, 25% are left unattempted and the rest are wrong. If the test has 80 questions, how many questions did the student answer wrongly?

  1. 20
  2. 16
  3. 24
  4. 12 Correct answer.

Explanation

Correct answers = 60% of 80 = 48, leaving 32 questions. Of these, 25% are unattempted = 8, so wrong answers = 32 − 8 = 24. This uses successive percentage application on the remainder.

Question 31Aptitude

In an IPMAT Indore reasoning puzzle, a code assigns each letter its position in the alphabet, and a word's value is the sum of its letters' positions. If the value of 'CAT' is 24, what is the value of 'DOG'?

  1. 32
  2. 26 Correct answer.
  3. 24
  4. 30

Explanation

Using alphabet positions, D=4, O=15, G=7, so the sum is 4+15+7 = 26. The check with CAT (3+1+20 = 24) confirms the rule.

Question 32Aptitude

A clock in the exam hall shows 3:30. What is the smaller angle between the hour hand and the minute hand at that moment?

  1. 80°
  2. 90°
  3. 85°
  4. 75° Correct answer.

Explanation

At 3:30, the minute hand is at 6 (180°) and the hour hand has moved 3.5 hours from 12, i.e. 3.5 × 30° = 105°. The difference is 180° − 105° = 75°.

Question 33Aptitude

A candidate's reading comprehension accuracy improves from 40% to 60% on a 50-question passage set. What is the percentage increase in the number of correct answers?

  1. 33.3%
  2. 20%
  3. 50% Correct answer.
  4. 25%

Explanation

Correct answers rise from 20 to 30, an increase of 10. The percentage increase is (10/20) × 100 = 50%, computed on the original number correct.

Question 34Aptitude

In an IPMAT-style arrangement puzzle, five books P, Q, R, S, T are placed in a row. Q is immediately to the right of P, and S is at one end. If T is at the other end and R is in the middle, which book is immediately to the left of R?

  1. P
  2. S
  3. Q Correct answer.
  4. T

Explanation

With S at one end, T at the other, and R in the middle position (third), the remaining slots are second and fourth for P and Q. Since Q is immediately right of P, P is second and Q is fourth, so Q is not left of R; instead P sits immediately left of R. Rechecking: positions are S, P, R, Q, T, so the book immediately left of R is P.

Question 35Aptitude

A number series in an IPMAT mock reads 2, 6, 12, 20, 30, ... What is the next term?

  1. 42 Correct answer.
  2. 40
  3. 44
  4. 36

Explanation

The differences are 4, 6, 8, 10, which increase by 2 each time, so the next difference is 12. Adding 12 to 30 gives 42.

Question 36Aptitude

A candidate must select 3 topics out of 6 for a group discussion in the IPMAT interview round, but two specific topics cannot be selected together. In how many ways can the selection be made?

  1. 16 Correct answer.
  2. 18
  3. 20
  4. 12

Explanation

Total selections of 3 from 6 = 20. Selections containing both forbidden topics require choosing 1 more from the remaining 4, giving 4 such cases. So valid selections = 20 − 4 = 16.

Question 37Aptitude

A student's score in a mock is increased by 20% and then reduced by 20% on the new score. If the final score is 96, what was the original score?

  1. 96
  2. 104
  3. 120
  4. 100 Correct answer.

Explanation

A 20% increase followed by a 20% decrease multiplies the score by 1.2 × 0.8 = 0.96. So original × 0.96 = 96, giving original = 100.

Question 38Aptitude

In a data interpretation set, a pie chart shows how 720 candidates distributed their preparation time across four sections. If the Verbal Ability sector has a central angle of 90°, how many candidates focused on Verbal Ability?

  1. 160
  2. 200
  3. 180 Correct answer.
  4. 240

Explanation

A sector angle of 90° represents 90/360 = 1/4 of the total. One quarter of 720 is 180 candidates.

Question 39Aptitude

A train of length 150 m crosses a platform of length 250 m in 20 seconds. What is the speed of the train in km/h?

  1. 72 Correct answer.
  2. 90
  3. 80
  4. 60

Explanation

Total distance = 150 + 250 = 400 m in 20 s, so speed = 20 m/s. Converting to km/h: 20 × 18/5 = 72 km/h.

Question 40Aptitude

If the average of 10 numbers is 25, and the average of 8 of them is 24, what is the average of the remaining 2 numbers?

  1. 30
  2. 29 Correct answer.
  3. 27
  4. 28

Explanation

Total of 10 numbers = 250, and total of 8 numbers = 192, so the remaining two sum to 58. Their average is 58/2 = 29.

Question 41Aptitude

A statement in an IPMAT-style critical reasoning set says: 'Students who practise timed mocks score higher on average.' Which of the following, if true, most weakens this claim?

  1. Students who already score higher tend to choose timed mocks. Correct answer.
  2. Some students who practise timed mocks score low.
  3. Timed mocks are available online.
  4. Mock tests cover the same syllabus as the exam.

Explanation

If high scorers self-select into timed mocks, the correlation may reflect pre-existing ability rather than a benefit of mocks. This reverses the causal direction and weakens the claim. The other options do not challenge the causal link.

Question 42Aptitude

A geometric figure in an IPMAT aptitude set is a rectangle whose length is increased by 25% and breadth decreased by 20%. What is the percentage change in area?

  1. 10% increase
  2. 5% decrease
  3. No change Correct answer.
  4. 5% increase

Explanation

New area factor = 1.25 × 0.80 = 1.00, so area is unchanged. Equal percentage changes in opposite directions on the two dimensions cancel.

Question 43Aptitude

A candidate's probability of clearing the IPMAT written round is 0.6, and, given that, the probability of clearing the interview is 0.5. What is the probability of clearing both rounds?

  1. 0.8
  2. 0.5
  3. 0.3 Correct answer.
  4. 0.11

Explanation

For dependent events, P(both) = P(written) × P(interview | written) = 0.6 × 0.5 = 0.3. Multiplying conditional probabilities is the correct rule.

Question 44Aptitude

A sum invested at compound interest doubles in 4 years. In how many years will it become 8 times itself at the same rate?

  1. 16
  2. 12 Correct answer.
  3. 10
  4. 8

Explanation

Doubling takes 4 years, so each 4-year block doubles the amount. To reach 8 times, three doublings are needed (2³ = 8), taking 3 × 4 = 12 years.

Question 45Aptitude

If x² − 5x + 6 = 0 and x > 2, what is the value of x?

  1. 2
  2. 6
  3. 1
  4. 3 Correct answer.

Explanation

Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3. The condition x > 2 leaves x = 3.

Question 46Aptitude

In a coding-decoding question, 'EXAM' is written as 'FYBN'. Using the same rule, how is 'TEST' written?

  1. SFST
  2. UFTT
  3. UFTU Correct answer.
  4. UETU

Explanation

Each letter is shifted one place forward in the alphabet: E→F, X→Y, A→B, M→N. Applying this to TEST gives U, F, T, U, i.e. UFTU.

Question 47Aptitude

A shopkeeper marks an item at ₹400 and offers a discount of 15%, still earning a profit of 20% on cost. What is the cost price?

  1. ₹250
  2. ₹300
  3. ₹283.33 Correct answer.
  4. ₹320

Explanation

Selling price after discount = 85% of 400 = ₹340. If this is 20% above cost, cost = 340/1.2 ≈ ₹283.33.

Question 48Aptitude

A sequence follows the rule: each term after the first is obtained by multiplying the previous term by 2 and subtracting 1. If the first term is 3, what is the fourth term?

  1. 21
  2. 15
  3. 19
  4. 17 Correct answer.

Explanation

Starting at 3: second term = 2×3 − 1 = 5; third = 2×5 − 1 = 9; fourth = 2×9 − 1 = 17. Applying the rule step by step gives 17.

Question 49Aptitude

In a Venn diagram of 100 candidates, 60 prepared for Quantitative Ability, 50 for Verbal Ability, and 20 prepared for both. How many prepared for neither?

  1. 10 Correct answer.
  2. 40
  3. 20
  4. 30

Explanation

By inclusion–exclusion, candidates preparing for at least one = 60 + 50 − 20 = 90. Hence neither = 100 − 90 = 10.

Question 50Aptitude

A cube is painted on all faces and then cut into 27 equal smaller cubes. How many smaller cubes have exactly two painted faces?

  1. 12 Correct answer.
  2. 6
  3. 24
  4. 8

Explanation

In a 3×3×3 cube, cubes with exactly two painted faces lie along the edges but not at the corners. There are 12 edges, each contributing one such cube, giving 12.