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
Statement 1 : if\(a=5\) and\(b=1\) , then\(2ab\) is divisible by\(5\) but\(a^2+b^2\) is not, where as if\(a=b=5\) , then both\(2ab\) and\(a^2+b^2\) is divisible by\(5\) . HenceInsufficient
Statement 2 if\(a=b=5\) , then both\(a-b\) &\(a^2+b^2\) is divisible by\(5\) , but if\(a=6\) and\(b=1\) , then\(a-b\) is divisible by\(5\) but\(a^2+b^2\) is not. HenceInsufficient
Combining 1 & 2, we can write\( a^2+b^2=(a-b)^2+2ab\)
...