The sum of two positive integers 'a' and 'b' is 528 and their HCF is 33. Which of the following cannot be the value of (a - b)? (A) 396 (B) 264 (C) 6 (D) 33

1 Answer
Aug 9, 2018

The right option is (C) 66.

Explanation:

The HCF of a, b in NN is 33.

:. a=33x and b=33y for some x,y in NN.

Utilising this in the Given that a+b=528, we have,

33x+33y=528.

Now, a-b=33x-33y=33(x-y)=33m," say, "m in NN.

This shows that (a-b) must be a multiple of 33.

Therefore, the right option is (C) 6.