Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is C 4

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).
The 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