Question

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

Answer 1

The correct option is A 4

The sum of two numbers is 528.
H.C.F of two numbers = 33
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).
Therefore, required numbers are (33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)
The number of such pairs is 4.