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Quantitative Aptitude — HCM
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Quantitative Aptitude — HCM

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8 mins
Time
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10
Questions
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1
Per Q

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Quantitative Aptitude — HCM — Questions with Answers Open after you finish the quiz — all 10 questions, with answers and explanations.
Q1. Find the HCF of 24 and 36.
  1. A) 6
  2. B) 12
  3. C) 18
  4. D) 24
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Answer: B. B) 12
The HCF of 24 (2³ × 3) and 36 (2² × 3²) is 2² × 3 = 12.
Q2. What is the HCF of 42, 63, and 105?
  1. A) 7
  2. B) 14
  3. C) 21
  4. D) 35
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Answer: C. C) 21
The prime factorization of 42 = 2 × 3 × 7, 63 = 3² × 7, and 105 = 3 × 5 × 7. The common factors are 3 and 7, so HCF = 3 × 7 = 21.
Q3. Find the HCF of the fractions ⁶⁄₇, ⁹⁄₁₄, and ¹⁵⁄₂₁.
  1. A) ¹⁄₁₄
  2. B) ³⁄₁₄
  3. C) ¹⁄₇
  4. D) ³⁄₇
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Answer: A. A) ¹⁄₁₄
HCF of fractions = (HCF of numerators) ÷ (LCM of denominators). HCF(6, 9, 15) = 3. LCM(7, 14, 21) = 42. So, HCF = ³⁄₄₂ = ¹⁄₁₄.
Q4. What is the HCF of 0.5, 1.25, and 0.75?
  1. A) 0.05
  2. B) 0.15
  3. C) 0.20
  4. D) 0.25
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Answer: D. D) 0.25
Convert decimals to integers by multiplying by 100: 50, 125, 75. HCF(50, 125, 75) = 25. Divide by 100 to get 0.25.
Q5. Find the greatest number that divides 48 and 72 exactly.
  1. A) 24
  2. B) 12
  3. C) 16
  4. D) 8
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Answer: A. A) 24
The greatest number that divides two numbers exactly is their HCF. HCF(48, 72) = 24.
Q6. Three containers have capacities of 105 litres, 140 litres, and 175 litres. What is the maximum capacity of a measuring can that can measure the liquid of all three containers an exact number of times?
  1. A) 5 litres
  2. B) 7 litres
  3. C) 35 litres
  4. D) 70 litres
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Answer: C. C) 35 litres
The maximum capacity will be the HCF of 105, 140, and 175. HCF(105, 140, 175) = 35.
Q7. The product of two numbers is 2160 and their HCF is 12. What is their LCM?
  1. A) 120
  2. B) 150
  3. C) 180
  4. D) 240
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Answer: C. C) 180
For two numbers, Product = HCF × LCM. So, LCM = Product ÷ HCF = 2160 ÷ 12 = 180.
Q8. Find the greatest number that divides 130 and 190 leaving the same remainder 10 in each case.
  1. A) 30
  2. B) 40
  3. C) 50
  4. D) 60
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Answer: D. D) 60
The required number is the HCF of (130 - 10) and (190 - 10), i.e., HCF(120, 180) = 60.
Q9. Find the greatest number that divides 1657 and 2037 leaving remainders 6 and 5 respectively.
  1. A) 127
  2. B) 131
  3. C) 137
  4. D) 141
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Answer: A. A) 127
The required number is the HCF of (1657 - 6) and (2037 - 5), i.e., HCF(1651, 2032) = 127.
Q10. Find the HCF of 2³ × 3² × 5¹ and 2² × 3³ × 5².
  1. A) 2³ × 3³ × 5²
  2. B) 2² × 3² × 5¹
  3. C) 2³ × 3² × 5²
  4. D) 2² × 3³ × 5¹
Show answer
Answer: B. B) 2² × 3² × 5¹
The HCF of numbers expressed as prime factors is found by taking the lowest power of each common prime factor. Here, HCF = 2² × 3² × 5¹.
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