Bunuel wrote:

If \(a\) and \(b\) are positive integers, is \(a^2 + b^2\) divisible by 5?

(1) \(2ab\) is divisible by 5

(2) \(a - b\) is divisible by 5

M19-11

Yes no type Qs, a

Given info- a and b are positive integer then a2+b2/5 =integer??

St-1 2ab is divisible by 5, then a is multiple of 5 or b is multiple of 5 or both a & b is multiple of 5.

If a& b both multiple of 5 then sufficient if a only or b only is multiple then insufficient.

St-2 a-b is multiple of 5, a and b both multiple of 5 then sufficient also a and b can not be multiple of 5 eg. 8-3 is divisible by 5. insufficient.

Combine--If either a or b is multiple of 5 then other one has to be multiple of 5 to satisfy a-b is multiple of 5. then sufficient.

if a is 10 and b is 2 then a-b can not be divisible by 5. for both statement true and a and b has to be multiple of 5.

Answer is C