If x and y are positive integers , is x^y + (x^x)(y^y) odd?

Question

If x and y are positive integers , is  x^y + (x^x)(y^y)  odd?

(1) x + 2y is odd
(2) y + 2x is odd

PyjamaScientist · Answer

Is  x^y + (x^x)(y^y)  odd?
For this to be odd, either of  x^y  &  (x^x)(y^y)  needs to be odd and the other even.
But, since 'x' is present on both sides, 'x' can not be even, otherwise both the terms would be even. Thus, x has to be odd, and y has to be even. If we can prove this, it will answer our question: Is  x^y + (x^x)(y^y)  odd?

(1) x + 2y is odd.
For this to be odd, x has to be odd. We do not know the nature of y. y can be either even or odd. Insufficient.

(2) y + 2x is odd.
For this to be odd, y has to be odd. x can be even or odd. Insufficient.

(1) + (2),
x and y both are odd. Thus,  x^y + (x^x)(y^y)  will be even, because odd + odd = even.
Thus is sufficient to answer the question, Is  x^y + (x^x)(y^y)  odd? No.  (C)

sanjitscorps18 · Answer

If x and y are positive integers , is x^y+(x^x)(y^y) odd?

Essentially asking two possibilities
1. If x is odd and y is even then x^y+(x^x)(y^y) becomes odd + odd x even = odd
or
2. If y is odd. In this case we have two cases
 a. If x is even then x^y+(x^x)(y^y) becomes even + odd x even = even
 b. If x is odd then x^y+(x^x)(y^y) becomes odd + odd x odd = even
Hence we can definitely prove that x^y+(x^x)(y^y) is not odd

irrespective of x being odd or even the answer is always even
(1) x + 2y is odd
Here x is odd but we don't know anything about y. Insufficient

(2) y + 2x is odd
Here y is odd.
As noted above, when y is odd, whether x is odd or even, the expression x^y+(x^x)(y^y) is always even. Hence this is sufficient to prove a Yes/No question

Option B

IanStewart · Answer

You've determined at the outset the conditions under which the answer to the question will be 'yes'. But if we learn from one statement that those conditions are not satisfied, we can then be sure the answer to the question is 'no', and that's all we need in DS: to be certain of the answer to the question. That's what happens with Statement 2: we learn y is odd, so y is certainly not even, and so the answer to the question must be 'no', and Statement 2 is sufficient.

The exponents in this question aren't going to change anything about evenness or oddness, so the question is really asking if x + xy is odd, or if x(y + 1) is odd. Statement 1 tells us x is odd, but we don't know about y+1. Statement 2 tells us y is odd, so y+1 is even, and x(y+1) must be even, so the answer to the question must be 'no', and the answer is B.

felon57 · Answer

for statement 2, we don't know if x is ever or odd, but we need x to be odd, should be insufficient.

If x and y are positive integers , is x^y + (x^x)(y^y) odd?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards