A number consists of two digits. The sum of digits is 12 and the number is 6 more than 6 times the units digit. Find the number.

The correct answer is D: 84. Let tens digit = x, units digit = y. Then x + y = 12 and 10x + y = 6y + 6. From second: 10x = 5y + 6. Substituting y = 12-x: 10x = 5(12-x) + 6 = 60 - 5x + 6. So 15x = 66, x = 8, y = 4. Number = 84

What is the smallest natural number that has exactly 10 divisors?

The correct answer is A: 48. For a number n = p₁^a₁ × p₂^a₂..., number of divisors = (a₁+1)(a₂+1)... We need (a₁+1)(a₂+1)... = 10 = 10×1 or 5×2. Testing: 2^9 = 512, 2^4×3 = 48. 48 has divisors: 1,2,3,4,6,8,12,16,24,48 = 10 divisors.

If a number is represented as 2³ × 3² × 5¹, how many divisors does it have?

The correct answer is C: 24. Number of divisors = (3+1)(2+1)(1+1) = 4 × 3 × 2 = 24.

The GCD of two numbers is 12 and their LCM is 144. If one number is 36, find the other number.

The correct answer is A: 48. Using the property: GCD(a,b) × LCM(a,b) = a × b. Therefore: 12 × 144 = 36 × b. So 1728 = 36b, which gives b = 48.

If the sum of two numbers is 50 and their product is 600, what are the numbers?

The correct answer is A: 20 and 30. Let numbers be x and y. x + y = 50 and xy = 600. From x + y = 50, y = 50 - x. Substituting: x(50-x) = 600, giving x^2 - 50x + 600 = 0. Using quadratic formula or factoring: (x-20)(x-30) = 0, so x = 20, y = 30

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Quantitative Aptitude
HCF and LCM

Quantitative aptitude questions for competitive exams

61 Q 7 Topics Take Mock Test

Difficulty: All Easy Medium Hard 31–40 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.31 Easy HCF and LCM

A shopkeeper buys books at ₹20 each and sells at a profit of 25%. During a sale, he gives a 10% discount. What is his effective profit percentage?

A 12.5%

B 15%

C 11.25%

D 13.75%

Correct Answer: A. 12.5%

EXPLANATION

SP = 20 × 1.25 = ₹25; After 10% discount = 25 × 0.9 = ₹22.5; Profit% = (22.5-20)/20 × 100 = 12.5%

Test

Q.32 Easy HCF and LCM

Three bells ring at intervals of 6, 9, and 15 minutes respectively. They ring together at 9:00 AM. At what time will they ring together again?

A 9:45 AM

B 10:00 AM

C 9:30 AM

D 10:30 AM

Correct Answer: D. 10:30 AM

EXPLANATION

LCM of 6, 9, 15 = 90 minutes = 1 hour 30 minutes. So they ring together at 10:30 AM

Test

Q.33 Easy HCF and LCM

The HCF of two numbers is 18 and their LCM is 1080. If one number is 108, find the other number.

A 180

B 162

C 216

D 144

Correct Answer: A. 180

EXPLANATION

Using HCF × LCM = Product of two numbers: 18 × 1080 = 108 × x; x = 19440/108 = 180

Test

Q.34 Easy HCF and LCM

HCF of two numbers is 16. Their LCM is 960. Find the product of the numbers.

A 15,360

B 16,384

C 18,432

D 20,480

Correct Answer: A. 15,360

EXPLANATION

HCF×LCM = product of numbers. 16×960 = 15,360.

Test

Q.35 Easy HCF and LCM

A man walks 5 km/h and covers a distance in 6 hours. If he walks at 6 km/h, how much time saved?

A 0.5 hour

B 1 hour

C 1.5 hours

D 2 hours

Correct Answer: B. 1 hour

EXPLANATION

Distance = 5×6 = 30 km. New time = 30/6 = 5 hours. Time saved = 6-5 = 1 hour.

Test

Q.36 Easy HCF and LCM

A man's salary increases from ₹40,000 to ₹48,000. What is the percentage increase?

A 15%

B 18%

C 20%

D 22%

Correct Answer: C. 20%

EXPLANATION

Increase = 48000 - 40000 = 8000. Percentage = 8000/40000 × 100 = 20%.

Test

Q.37 Easy HCF and LCM

A shopkeeper buys goods at ₹80 and marks it up by 25%. After giving 10% discount, what is his profit percentage?

A 10.5%

B 12.5%

C 15%

D 17.5%

Correct Answer: B. 12.5%

EXPLANATION

MP = 80×1.25 = ₹100. SP = 100×0.9 = ₹90. Profit = 10/80 × 100 = 12.5%.

Test

Q.38 Easy HCF and LCM

A boat covers 24 km upstream in 6 hours and 24 km downstream in 3 hours. Find the speed of the current.

A 2 km/h

B 3 km/h

C 4 km/h

D 5 km/h

Correct Answer: A. 2 km/h

EXPLANATION

Upstream speed = 24/6 = 4 km/h. Downstream speed = 24/3 = 8 km/h. Current = (8-4)/2 = 2 km/h.

Test

Q.39 Easy HCF and LCM

A train 150m long crosses a platform of 250m in 20 seconds. Find its speed in km/h.

A 54 km/h

B 72 km/h

C 81 km/h

D 90 km/h

Correct Answer: B. 72 km/h

EXPLANATION

Distance = 150 + 250 = 400m. Speed = 400/20 = 20 m/s = 20×3.6 = 72 km/h.

Test

Q.40 Easy HCF and LCM

Two pipes A and B fill a tank in 20 and 30 minutes respectively. A leak empties it in 60 minutes. How long to fill the tank with all three?

A 15 minutes

B 18 minutes

C 12 minutes

D 20 minutes

Correct Answer: A. 15 minutes

EXPLANATION

Rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 minutes.

Test

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Quantitative Aptitude HCF and LCM

Quantitative Aptitude
HCF and LCM