Free Quantitative Aptitude questions with answers for MBA CET

Arithmetic, algebra, geometry, number systems, permutation and combination, probability and data interpretation - the quant questions that decide your MBA CET percentile. These 117 questions are also useful for CAT, MAT and ATMA. Tap “Show answer” under any question for the correct option and the explanation.

Question 101
If x + 1/x = 5, then find x³ + 1/x³.
- (A)95
- (B)100
- (C)105
- (D)110
- (E)115
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Correct answer: (D) 110
x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x) = 5³ - 3x5 = 125 - 15 = 110.
Question 102
The diagonal of a rectangle is 25 cm and its area is 168 cm². What is its perimeter?
- (A)56 cm
- (B)60 cm
- (C)62 cm
- (D)64 cm
- (E)66 cm
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Correct answer: (C) 62 cm
With diagonal d and sides a, b: a² + b² = 625 and ab = 168. Then (a+b)² = a² + b² + 2ab = 625 + 336 = 961, so a+b = 31. Perimeter = 2(a+b) = 62 cm.
Question 103
The radius of a cylinder is increased by 20%. By approximately what percentage must its height be reduced so that its volume remains unchanged?
- (A)25%
- (B)27.78%
- (C)30.56%
- (D)33⅓%
- (E)36%
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Correct answer: (C) 30.56%
Volume = πr²h must stay constant. With r increased to 1.2r, the new height h' = h/(1.2)² = h/1.44 = 0.6944h, a reduction of about 30.56%.
Question 104
How many distinct arrangements can be made using all the letters of the word MANAGEMENT?
- (A)113,400
- (B)151,200
- (C)181,440
- (D)226,800
- (E)453,600
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Correct answer: (D) 226,800
MANAGEMENT has 10 letters with M, A, N, E each repeated twice (and G, T once each). Distinct arrangements = 10!/(2!x2!x2!x2!) = 3,628,800/16 = 226,800.
Question 105
Two fair dice are thrown simultaneously. What is the probability that the product of the numbers obtained is divisible by 6?
- (A)1/3
- (B)5/12
- (C)4/9
- (D)1/2
- (E)7/12
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Correct answer: (B) 5/12
Out of 36 equally likely outcomes, the pairs (a,b) where a x b is divisible by 6 total 15. Probability = 15/36 = 5/12.
Question 106
A shopkeeper marks an article 50% above its cost price and offers a discount of 20%, earning a certain profit. Later, the cost price increases by 25%, but the marked price remains unchanged. What discount should the shopkeeper now offer to earn exactly the same absolute profit as before?
- (A)2½%
- (B)3⅓%
- (C)5%
- (D)6⅔%
- (E)8%
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Correct answer: (B) 3⅓%
Take the original cost price as 100. Marked price = 150. Selling price after a 20% discount = 150 × 0.8 = 120. Profit = 120 – 100 = 20. New cost price = 100 × 1.25 = 125. The marked price is still 150. To earn the same absolute profit of 20, the selling price must be 125 + 20 = 145. Discount = 150 – 145 = 5, so the discount percentage = 5/150 × 100 = 3⅓%.
Question 107
An alloy contains copper and zinc in the ratio 5:3. A manufacturer removes 12 kg of the alloy and replaces it with 12 kg of pure copper. The resulting ratio of copper to zinc becomes 7:3. What was the original weight of the alloy?
- (A)48 kg
- (B)54 kg
- (C)56 kg
- (D)60 kg
- (E)72 kg
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Correct answer: (D) 60 kg
Let the original weight be W kg. Copper = 5W/8 and zinc = 3W/8. The 12 kg removed contains copper 12 × 5/8 = 7.5 kg and zinc 12 × 3/8 = 4.5 kg. After replacing it with 12 kg of copper: copper = 5W/8 – 7.5 + 12 = 5W/8 + 4.5, zinc = 3W/8 – 4.5. Ratio 7:3 gives 3(5W/8 + 4.5) = 7(3W/8 – 4.5). 15W/8 + 13.5 = 21W/8 – 31.5, so 45 = 6W/8, and W = 60 kg. Check: copper = 37.5 + 4.5 = 42, zinc = 22.5 – 4.5 = 18, ratio 42:18 = 7:3.
Question 108
A and B together can complete a project in 12 days, B and C together in 15 days, and C and A together in 20 days. A works alone for 6 days, followed by B working alone for 8 days. How many additional days will C, working alone, require to complete the remaining project?
- (A)12 days
- (B)18 days
- (C)24 days
- (D)30 days
- (E)36 days
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Correct answer: (C) 24 days
Daily work: A + B = 1/12, B + C = 1/15, C + A = 1/20. Adding: 2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 1/5, so A + B + C = 1/10. C = 1/10 – 1/12 = 1/60, A = 1/10 – 1/15 = 1/30, B = 1/10 – 1/20 = 1/20. Work done by A in 6 days = 6/30 = 1/5. Work done by B in 8 days = 8/20 = 2/5. Total done = 3/5. Remaining = 2/5. C needs (2/5) ÷ (1/60) = 24 days.
Question 109
A train 180 metres long crosses a platform 270 metres long in 18 seconds. The same train overtakes another train, 120 metres long and travelling in the same direction, in 30 seconds. What is the speed of the slower train?
- (A)54 km/h
- (B)48 km/h
- (C)60 km/h
- (D)66 km/h
- (E)72 km/h
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Correct answer: (A) 54 km/h
To cross the platform the train covers 180 + 270 = 450 m in 18 s, so its speed = 25 m/s = 90 km/h. To overtake the other train it must cover 180 + 120 = 300 m in 30 s, so the relative speed = 10 m/s. Speed of the slower train = 25 – 10 = 15 m/s = 15 × 18/5 = 54 km/h.
Question 110
If $x$ is a real number satisfying $x^{2} - 5 x + 1 = 0$ find the value of $x^{4} + \frac{1}{x ^{4}}$
- (A)521
- (B)523
- (C)525
- (D)529
- (E)527
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Correct answer: (E) 527
Since x ≠ 0, divide the equation by x: x + 1/x = 5. Square it: x² + 1/x² = 25 – 2 = 23. Square again: x⁴ + 1/x⁴ = 23² – 2 = 529 – 2 = 527.
Question 111
A positive integer $N$ is divisible by 72 and has exactly 24 distinct positive factors. If its only prime factors are 2 and 3, what is the smallest possible value of $N$ ?
- (A)576
- (B)768
- (C)864
- (D)1152
- (E)1944
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Correct answer: (C) 864
72 = 2³ × 3², so N = 2ᵃ × 3ᵇ with a ≥ 3 and b ≥ 2. The number of factors is (a + 1)(b + 1) = 24, with a + 1 ≥ 4 and b + 1 ≥ 3. The possible pairs (a + 1, b + 1) are (4, 6), (6, 4) and (8, 3): (a, b) = (3, 5): N = 8 × 243 = 1944 (a, b) = (5, 3): N = 32 × 27 = 864 (a, b) = (7, 2): N = 128 × 9 = 1152 The smallest is 864. Check the others: 576 = 2⁶ × 3² has only 7 × 3 = 21 factors, and 768 = 2⁸ × 3 is not divisible by 9.
Question 112
The equation $t^{2} - 7 t + k = 0$ has two distinct positive roots $α$ and $β$ . If $α^{3} + β^{3} = 133$ , find the value of $k$ .
- (A)9
- (B)10
- (C)11
- (D)12
- (E)13
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Correct answer: (B) 10
Sum of roots α + β = 7 and product αβ = k. α³ + β³ = (α + β)³ – 3αβ(α + β) = 343 – 21k. 343 – 21k = 133, so 21k = 210 and k = 10. Check: t² – 7t + 10 = 0 gives roots 2 and 5, which are distinct and positive, and 8 + 125 = 133.
Question 113
A triangle has sides measuring 13 cm, 14 cm and 15 cm. What is the ratio of its inradius to its circumradius?
- (A)16/65
- (B)24/65
- (C)8/13
- (D)32/65
- (E)4/13
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Correct answer: (D) 32/65
Semi-perimeter s = (13 + 14 + 15)/2 = 21. Area = √[21 × 8 × 7 × 6] = √7056 = 84 cm². Inradius r = Area/s = 84/21 = 4 cm. Circumradius R = abc/(4 × Area) = (13 × 14 × 15)/(4 × 84) = 2730/336 = 65/8 cm. r : R = 4 ÷ (65/8) = 32/65.
Question 114
In how many distinct ways can the letters of the word BALLOON be arranged such that no two vowels are adjacent?
- (A)360
- (B)300
- (C)420
- (D)480
- (E)240
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Correct answer: (A) 360
BALLOON has 7 letters: the consonants B, L, L, N (4 letters) and the vowels A, O, O (3 letters). Arrange the consonants first: 4!/2! = 12 ways (the two Ls are identical). They create 5 gaps (including both ends). Choose 3 gaps for the vowels: ⁵C₃ = 10 ways. Arrange the vowels in the chosen gaps: 3!/2! = 3 ways (the two Os are identical). Total = 12 × 10 × 3 = 360.
Question 115
A bag contains 4 red, 5 blue and 3 green balls. Two balls are drawn randomly without replacement. Given that at least one ball drawn is red, what is the probability that the two balls are of different colours?
- (A)4/5
- (B)8/11
- (C)9/11
- (D)17/19
- (E)16/19
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Correct answer: (E) 16/19
There are 12 balls, so the total number of pairs is ¹²C₂ = 66. Pairs with no red ball: ⁸C₂ = 28, so pairs with at least one red ball = 66 – 28 = 38. Among these 38 pairs, the two balls have different colours when one is red and the other is not: 4 × 8 = 32 pairs. (The remaining 6 pairs are both red.) Required probability = 32/38 = 16/19.
Question 116
What is the value of the real number $x$ ? Statement I: $x^{2} - 7 x + 12 = 0$ Statement II: $x^{2} - 5 x + 6 = 0$ Select the correct option.
- (A)Statement I alone is sufficient, but Statement II alone is not sufficient.
- (B)Statement II alone is sufficient, but Statement I alone is not sufficient.
- (C)Both statements together are sufficient, but neither statement alone is sufficient.
- (D)Each statement alone is sufficient.
- (E)Even both statements together are insufficient.
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Correct answer: (C) Both statements together are sufficient, but neither statement alone is sufficient.
Statement I: (x – 3)(x – 4) = 0, so x = 3 or 4. Not a unique value. Statement II: (x – 2)(x – 3) = 0, so x = 2 or 3. Not a unique value. Together, x must satisfy both, so the common root is x = 3 only. This gives a unique value. So both statements together are sufficient, but neither alone is.
Question 117
Three positive integers are in geometric progression. Their sum is 26, and their product is 216. What is the largest of the three integers?
- (A)12
- (B)14
- (C)16
- (D)20
- (E)18
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Correct answer: (E) 18
Let the three terms be a/r, a and ar. Their product is a³ = 216, so a = 6. The sum gives 6/r + 6 + 6r = 26, so 6/r + 6r = 20, that is 3r² – 10r + 3 = 0. (3r – 1)(r – 3) = 0, so r = 3 or r = 1/3. Both give the numbers 2, 6 and 18. Check: 2 + 6 + 18 = 26 and 2 × 6 × 18 = 216. The largest is 18.

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