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Question (11)

QN0030563

A number is divisible by both 12 and 18. Which of the following cannot be the number?

(A) 72
(B) 108
(C) 126
(D) 180

Correct Answer: C

Explanation:

The number must be divisible by LCM(12,18) = 36. 126 is not divisible by 36.

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Question (12)

QN0030564

Which of the following numbers has exactly four factors?

(A) 15
(B) 16
(C) 18
(D) 25

Correct Answer: A

Explanation:

Factors of 15 are 1, 3, 5 and 15.

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Question (13)

QN0030565

The HCF of two numbers is 9 and their product is 2916. If their LCM is 324, the numbers satisfy which relation?

(A) HCF + LCM = Product
(B) HCF × LCM = Product of the numbers
(C) HCF − LCM = Product
(D) HCF = LCM

Correct Answer: B

Explanation:

9 × 324 = 2916.

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Question (14)

QN0030566

Which one of the following numbers is neither prime nor composite?

(A) 0
(B) 1
(C) 2
(D) 3

Correct Answer: B

Explanation:

The number 1 has only one factor.

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Question (15)

QN0030567

A factory packs 84 biscuits and 126 chocolates into identical gift boxes without mixing items. Each box must contain the greatest possible equal number of items of one kind. How many boxes are required altogether?

(A) 5
(B) 7
(C) 9
(D) 10

Correct Answer: A

Explanation:

HCF = 42. Total boxes = 84÷42 + 126÷42 = 5.

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Question (16)

QN0030568

Which of the following pairs has the smallest HCF?

(A) 24 and 36
(B) 35 and 64
(C) 42 and 56
(D) 45 and 60

Correct Answer: B

Explanation:

HCFs are 12, 1, 14 and 15 respectively.

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Question (17)

QN0030569

Find the least number that is divisible by 5, 6 and 8.

(A) 60
(B) 120
(C) 180
(D) 240

Correct Answer: B

Explanation:

LCM of 5, 6 and 8 is 120.

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Question (18)

QN0030570

Which statement is always true for any two positive integers?

(A) Their HCF is always a factor of their LCM.
(B) Their LCM is always smaller than both numbers.
(C) Their HCF is always a multiple of both numbers.
(D) Their product is always equal to their sum.

Correct Answer: A

Explanation:

The HCF always divides the LCM.

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Question (19)

QN0030571

A bell rings every 18 minutes, another every 24 minutes and a third every 30 minutes. If all ring together at 9:00 a.m., at what time will they next ring together?

(A) 1:00 p.m.
(B) 2:00 p.m.
(C) 3:00 p.m.
(D) 4:00 p.m.

Correct Answer: C

Explanation:

LCM of 18, 24 and 30 is 360 minutes = 6 hours. Next time = 3:00 p.m.

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Question (20)

QN0030572

Which of the following statements about prime factorisation is correct?

(A) Every composite number has a unique prime factorisation (apart from the order of factors).
(B) Every number has more than one prime factorisation.
(C) Prime numbers cannot be written using prime factors.
(D) Prime factorisation is possible only for even numbers.

Correct Answer: A

Explanation:

This is the Fundamental Theorem of Arithmetic.

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Question (11)

A number is divisible by both 12 and 18. Which of the following cannot be the number?

Explanation:

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Question (12)

Which of the following numbers has exactly four factors?

Explanation:

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Question (13)

The HCF of two numbers is 9 and their product is 2916. If their LCM is 324, the numbers satisfy which relation?

Explanation:

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Question (14)

Which one of the following numbers is neither prime nor composite?

Explanation:

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Question (15)

A factory packs 84 biscuits and 126 chocolates into identical gift boxes without mixing items. Each box must contain the greatest possible equal number of items of one kind. How many boxes are required altogether?

Explanation:

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Question (16)

Which of the following pairs has the smallest HCF?

Explanation:

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Question (17)

Find the least number that is divisible by 5, 6 and 8.

Explanation:

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Question (18)

Which statement is always true for any two positive integers?

Explanation:

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Question (19)

A bell rings every 18 minutes, another every 24 minutes and a third every 30 minutes. If all ring together at 9:00 a.m., at what time will they next ring together?

Explanation:

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Question (20)

Which of the following statements about prime factorisation is correct?

Explanation:

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