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__________?

A. 4
B. 6
C. 8
D. 12

Explanation:

Let the required numbers be 33a and 33b.

Then, 33a + 33b = 528 => a + b = 16.
Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9).
Required numbers are (33 * 1, 33 * 15), (33 * 3, 33 * 13), (33 * 5, 33 * 11), (33 * 7, 33 * 9).
The number of such pairs is 4.