EWT | Academic Question

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Question (31)
QN0030543
If the HCF of two numbers is equal to one of the numbers, then that number is:
  • (A) A multiple of the other number.
  • (B) A factor of the other number.
  • (C) Equal to the LCM.
  • (D) Always a prime number.

Correct Answer: B
Explanation:

The HCF equals the smaller number only when it is a factor of the other.

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Question (32)
QN0030544
Find the HCF and LCM of 30 and 45. Which option is correct?
  • (A) HCF = 5, LCM = 270
  • (B) HCF = 15, LCM = 90
  • (C) HCF = 10, LCM = 135
  • (D) HCF = 30, LCM = 45

Correct Answer: B
Explanation:

HCF = 15 and LCM = (30 × 45) ÷ 15 = 90.

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Question (33)
QN0030545
Which statement is true about the quicker procedure discussed for finding HCF and LCM?
  • (A) It helps determine both values more efficiently.
  • (B) It gives only the HCF.
  • (C) It is applicable only to three numbers.
  • (D) It works only when all numbers are prime.

Correct Answer: A
Explanation:

The procedure is designed to find both HCF and LCM efficiently.

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Question (34)
QN0030546
The HCF of two numbers is 12 and their LCM is 240. If one number is 48, the other number is:
  • (A) 50
  • (B) 60
  • (C) 72
  • (D) 84

Correct Answer: B
Explanation:

Other number = (12 × 240) ÷ 48 = 60.

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Question (35)
QN0030547
Which pair of numbers has HCF equal to 12?
  • (A) 36 and 48
  • (B) 30 and 42
  • (C) 45 and 60
  • (D) 28 and 56

Correct Answer: A
Explanation:

HCF of 36 and 48 is 12.

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Question (36)
QN0030548
Two numbers have HCF 8 and LCM 96. If one number is 24, the other number is:
  • (A) 28
  • (B) 30
  • (C) 32
  • (D) 36

Correct Answer: C
Explanation:

Other number = (8 × 96) ÷ 24 = 32.

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Question (37)
QN0030549
Which of the following statements is always correct?
  • (A) HCF is always greater than LCM.
  • (B) LCM is always smaller than HCF.
  • (C) HCF can never be greater than the smaller number.
  • (D) LCM is always equal to the sum of the numbers.

Correct Answer: C
Explanation:

The HCF cannot exceed the smaller of the two numbers.

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Question (38)
QN0030550
Find the HCF and LCM of 32 and 40. Which option is correct?
  • (A) HCF = 4, LCM = 320
  • (B) HCF = 8, LCM = 160
  • (C) HCF = 16, LCM = 80
  • (D) HCF = 8, LCM = 80

Correct Answer: B
Explanation:

HCF = 8 and LCM = (32 × 40) ÷ 8 = 160.

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Question (39)
QN0030551
If two numbers are co-prime, which relationship is always true?
  • (A) HCF = Product of the numbers
  • (B) LCM = Product of the numbers
  • (C) HCF = LCM
  • (D) LCM = Sum of the numbers

Correct Answer: B
Explanation:

For co-prime numbers, the LCM equals their product.

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Question (40)
QN0030552
Which property is used to verify the correctness of the HCF and LCM of two numbers?
  • (A) HCF + LCM = Product of the numbers
  • (B) HCF × LCM = Product of the numbers
  • (C) HCF − LCM = Difference of the numbers
  • (D) HCF ÷ LCM = Quotient of the numbers

Correct Answer: B
Explanation:

Product of the two numbers = HCF × LCM.

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