ziyuen wrote:

If a, b, and c are integers, is \((a+b)^2+c(a^2+b^2)\) an even number?

1) a and b are odd numbers

2) c is an odd number.

Hi ,

\(a^2+b^2\) will be same that is odd/ even as a+b would be..

So let's take TWO cases possible

A) a+b is Even, so \((a+b)^2+c(a^2+b^2)\) becomes E + c*E..

Both terms are even so total will be even, IRRESPECTIVE of c..

B) a+b is Odd, so \((a+b)^2+c(a^2+b^2)\) becomes Odd + c*Odd..

Both terms are Odd if c is odd so total will be even IRRESPECTIVE of a and b..

If c is Even, total becomes Odd+Even*Odd=Odd

Let's see the statements now..

I) a & b are odd, so a+b is Even

And TOTAL is Even as per case A.

Sufficient

II) c is odd...

If c is odd, irrespective of a and b , ans will be even as per case B.

Sufficient

D

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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