A man's income increases by 25%. If his new income is ₹62,500, what was his original income?

The correct answer is B: ₹50,000. New income = Original × 1.25. 62,500 = Original × 1.25. Original = 62,500/1.25 = ₹50,000

If 30% of a number is 120, what is 25% of that number?

The correct answer is C: 100. Number = 120/0.30 = 400. 25% of 400 = 100

A train travels at 60 km/h for 2 hours, then at 80 km/h for 3 hours. What is the average speed for the entire journey?

The correct answer is B: 72 km/h. Total distance = (60 × 2) + (80 × 3) = 120 + 240 = 360 km. Total time = 5 hours. Average speed = 360/5 = 72 km/h

Which of the following numbers is divisible by both 6 and 8?

The correct answer is A: 48. For divisibility by both 6 and 8, the number must be divisible by LCM(6,8) = 24. Check: 48 ÷ 24 = 2 ✓. Option A is correct.

The LCM of 15 and 25 is:

The correct answer is A: 75. This question asks us to find the Least Common Multiple (LCM) of two numbers using prime factorization. Step 1: Find prime factorization of 15 Break 15 into its prime factors. $$15 = 3 \times 5$$ Step 2: Find prime factorization of 25 Break 25 into its prime factors. $$25 = 5 \times 5 = 5^2$$ Step 3

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Quantitative Aptitude
HCF and LCM

Quantitative aptitude questions for competitive exams

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Difficulty: All Easy Medium Hard 21–30 of 61

Topics in Quantitative Aptitude

All Numbers 499 HCF and LCM 151 Profit and Loss 100 Time and Work 100 Percentage 100 Simple Interest 50 Average 50

Q.21 Easy HCF and LCM

The LCM of two coprime numbers is 143. If one number is 11, find the other.

A 13

B 15

C 17

D 19

Correct Answer: A. 13

EXPLANATION

For coprime numbers, HCF = 1. So LCM = Product. 143 = 11 × x. Therefore x = 13. Check: HCF(11,13) = 1 ✓

Test

Q.22 Easy HCF and LCM

HCF of two numbers is 11 and their sum is 99. If one number is 33, find the other number.

A 55

B 66

C 77

D 44

Correct Answer: B. 66

EXPLANATION

If HCF = 11, both numbers are multiples of 11. Sum = 99, one number = 33. Other = 99 - 33 = 66. Check: HCF(33,66) = 33. Correction: Numbers are 11×3=33 and 11×6=66. HCF = 11 ✓

Test

Q.23 Easy HCF and LCM

A product's cost price is ₹500. A trader marks it 60% above cost price and gives a discount of 25%. If HCF of profit and marked price is calculated, find the profit percentage.

A 20%

B 25%

C 30%

D 35%

Correct Answer: A. 20%

EXPLANATION

MP = 500 × 1.60 = ₹800. SP = 800 × 0.75 = ₹600. Profit = 100. Profit% = (100/500) × 100 = 20%

Test

Q.24 Easy HCF and LCM

Three numbers are in the ratio 2:3:4 and their LCM is 240. Find the HCF of these numbers.

A 20

B 30

C 15

D 10

Correct Answer: A. 20

EXPLANATION

Let numbers be 2k, 3k, 4k. LCM(2k, 3k, 4k) = 12k = 240, so k = 20. HCF = k = 20

Test

Q.25 Easy HCF and LCM

The HCF of two numbers is 12 and their LCM is 180. If one number is 36, find the other number.

A 60

B 48

C 72

D 84

Correct Answer: A. 60

EXPLANATION

Using HCF × LCM = Product of two numbers. 12 × 180 = 36 × x. Therefore x = 2160/36 = 60

Test

Q.26 Easy HCF and LCM

Three bells ring at 8, 12, and 18-minute intervals. After how many minutes will they ring together if they start together?

A 36 minutes

B 48 minutes

C 60 minutes

D 72 minutes

Correct Answer: D. 72 minutes

EXPLANATION

LCM(8, 12, 18) = LCM(2³, 2²×3, 2×3²) = 2³×3² = 8×9 = 72 minutes

Test

Q.27 Easy HCF and LCM

If a profit of ₹200 is made on a book by selling at 20% profit, what is the selling price?

A ₹1000

B ₹1200

C ₹1400

D ₹1500

Correct Answer: B. ₹1200

EXPLANATION

Profit = 20% of CP; ₹200 = 0.2×CP; CP = ₹1000; SP = 1000 + 200 = ₹1200

Test

Q.28 Easy HCF and LCM

A merchant offers successive discounts of 15% and 10%. What is the equivalent single discount?

A 23.5%

B 25%

C 24%

D 26.5%

Correct Answer: A. 23.5%

EXPLANATION

After 15% discount: 85%; After 10% on that: 85×90/100 = 76.5%; Single discount = 100-76.5 = 23.5%

Test

Q.29 Easy HCF and LCM

A worker can complete a job in 12 days. Another worker can complete it in 18 days. If they work together, how many days will they take?

A 6.5 days

B 7.2 days

C 8 days

D 9 days

Correct Answer: B. 7.2 days

EXPLANATION

Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36; Time = 36/5 = 7.2 days

Test

Q.30 Easy HCF and LCM

Find the LCM of 48, 64, and 96 using prime factorization.

A 192

B 288

C 384

D 576

Correct Answer: C. 384

EXPLANATION

48 = 2⁴×3; 64 = 2⁶; 96 = 2⁵×3; LCM = 2⁶×3 = 64×6 = 384

Test

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Quantitative Aptitude HCF and LCM

Quantitative Aptitude
HCF and LCM