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The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is__________?

Correct answer: A. 4

  • A. 4
  • B. 6
  • C. 8
  • D. 12

Explanation

Let the numbers be 33a and 33b. Then a + b = 528/33 = 16, and a and b must be co-prime because the H.C.F. is exactly 33. The positive pairs are (1,15), (3,13), (5,11) and (7,9), so there are 4 pairs. A student may count 6 by including pairs whose members have a common factor.

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