QA – Placement Quizzes | HCF | Question 10

The sum if two numbers is 528 and their HCF is 33. The number of pairs of numbers satisfying the above condition is:
(A) 4
(B) 6
(C) 8
(D) 12


Answer: (A)

Explanation: Let the required numbers be 33x and 33y. Then,
33x + 33y = 528
But, 528 = 2 * 2 * 2 * 2 * 3 * 11.
So, x + y = 16
Co-primes with the sum 16 are: (1, 15), (3, 13), (5, 11) and (7, 9). Hence, 4.

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