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Question (1)

QN0030553

The prime factorisation of a number is 2³ × 3 × 5. How many factors does the number have?

(A) 12
(B) 16
(C) 18
(D) 24

Correct Answer: B

Explanation:

Number of factors = (3 + 1)(1 + 1)(1 + 1) = 16.

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Question (2)

QN0030554

Which one of the following numbers is divisible by both 8 and 15?

(A) 110
(B) 180
(C) 240
(D) 280

Correct Answer: C

Explanation:

LCM of 8 and 15 is 120. Only 240 is a multiple of 120.

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Question (3)

QN0030555

A number leaves remainder 0 when divided by both 9 and 12. Which is the least possible value of the number?

(A) 18
(B) 24
(C) 36
(D) 108

Correct Answer: C

Explanation:

LCM of 9 and 12 is 36.

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Question (4)

QN0030556

Which of the following numbers has exactly three prime factors (not necessarily distinct)?

(A) 18
(B) 27
(C) 49
(D) 121

Correct Answer: A

Explanation:

18 = 2 × 3 × 3.

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Question (5)

QN0030557

Three ropes of lengths 36 m, 48 m and 60 m are to be cut into equal pieces of the greatest possible length. How many pieces will be obtained altogether?

(A) 10
(B) 11
(C) 12
(D) 15

Correct Answer: C

Explanation:

HCF = 12. Number of pieces = 3 + 4 + 5 = 12.

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Question (6)

QN0030558

Which statement is always true?

(A) Every multiple of a prime number is prime.
(B) Every factor of a composite number is composite.
(C) Every common multiple is a multiple of the LCM.
(D) Every common factor is equal to the HCF.

Correct Answer: C

Explanation:

Every common multiple is divisible by the LCM.

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Question (7)

QN0030559

Find the smallest number that must be added to 178 so that the result is divisible by both 6 and 8.

(A) 10
(B) 12
(C) 14
(D) 16

Correct Answer: C

Explanation:

LCM of 6 and 8 is 24. Next multiple after 178 is 192. Required addition = 14.

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Question (8)

QN0030560

Which one of the following pairs has the greatest LCM?

(A) 8 and 12
(B) 10 and 15
(C) 14 and 18
(D) 16 and 20

Correct Answer: C

Explanation:

LCMs are 24, 30, 126 and 80 respectively.

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Question (9)

QN0030561

The product of two numbers is 2520. Their HCF is 12. What is their LCM?

(A) 180
(B) 200
(C) 210
(D) 240

Correct Answer: C

Explanation:

LCM = 2520 ÷ 12 = 210.

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Question (10)

QN0030562

Two traffic signals turn green every 24 seconds and 40 seconds respectively. If they turn green together at 8:00:00 a.m., when will they next turn green together?

(A) 8:01:20 a.m.
(B) 8:02:00 a.m.
(C) 8:02:40 a.m.
(D) 8:03:20 a.m.

Correct Answer: B

Explanation:

LCM of 24 and 40 is 120 seconds = 2 minutes.

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Question (1)

The prime factorisation of a number is 2³ × 3 × 5. How many factors does the number have?

Explanation:

Link:

Question (2)

Which one of the following numbers is divisible by both 8 and 15?

Explanation:

Link:

Question (3)

A number leaves remainder 0 when divided by both 9 and 12. Which is the least possible value of the number?

Explanation:

Link:

Question (4)

Which of the following numbers has exactly three prime factors (not necessarily distinct)?

Explanation:

Link:

Question (5)

Three ropes of lengths 36 m, 48 m and 60 m are to be cut into equal pieces of the greatest possible length. How many pieces will be obtained altogether?

Explanation:

Link:

Question (6)

Which statement is always true?

Explanation:

Link:

Question (7)

Find the smallest number that must be added to 178 so that the result is divisible by both 6 and 8.

Explanation:

Link:

Question (8)

Which one of the following pairs has the greatest LCM?

Explanation:

Link:

Question (9)

The product of two numbers is 2520. Their HCF is 12. What is their LCM?

Explanation:

Link:

Question (10)

Two traffic signals turn green every 24 seconds and 40 seconds respectively. If they turn green together at 8:00:00 a.m., when will they next turn green together?

Explanation:

Link:

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