High School

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The H.C.F. of two numbers is 12, and their difference is 12. Which of the following can be the numbers?

A. 70, 84
B. 84, 96
C. 66, 77
D. 80, 92

Answer :

Final answer:

The numbers B. 84 and 96 are the correct pair as they both have an H.C.F. of 12 and a difference of 12, meeting the conditions specified in the question.

Explanation:

The question asks to find a pair of numbers whose Highest Common Factor (H.C.F.) is 12, and their difference is also 12. Since H.C.F. is a factor, both numbers must be multiples of 12. We will use this information to evaluate each pair of numbers provided in the options.

  • A. 70, 84: The difference is 14, which fails the requirement of a 12 difference. Also, 70 is not a multiple of 12.
  • B. 84, 96: The difference is 12, which fits the requirement, and both numbers are multiples of 12 (84 = 7 imes 12, 96 = 8 imes 12). This pair satisfies both conditions.
  • C. 66, 77: The difference is 11, not matching the 12 difference condition. Additionally, neither number is a multiple of 12.
  • D. 80, 92: The difference is 12, which fits the requirement, but 80 is not a multiple of 12.

Therefore, the pair that has both a difference of 12 and an H.C.F. of 12 is option B. 84, 96.

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