If x and y are integers, is |x| > |y|? 1) |x| = |y+1| 2)

I was reluctant to reply to this question for a long time because I don't like it all.

First of all: \(0^0\), in some sources equals to 1, some mathematicians say it's undefined. Anyway you won't need this for GMAT as the case of 0^0 is not tested on the GMAT.

Second: GMAT would give some constraints for unknowns in the stem (or at leas in second statement), for example:

As there is \(x!\) in statement (2) then in the stem (or at leas in second statement) GMAT most likely would specify that \(x\geq{0}\) as factorial of negative number is undefined;

Also as there is \(x^y\) in statement (2) then in the stem (or at leas in second statement) GMAT most likely would also specify that \(x\) and \(y\) can not be zero simultaneously as 0^0 is not tested on the GMAT.

So either we would have A. \(x\geq{0}\) and \(y\neq{0}\) OR B. \(x>0\).

If we place these constraint in the stem the question will be completely changed (no need for |x| in the stem and statement 1.) so we should place either of them them in statement 2.

So the question could be for example:

If \(x\) and \(y\) are integers, is \(|x|>|y|\)?

(1) \(|x| = |y+1|\). Clearly insufficient.

(2) \(x>{0}\) and \(x^y = x! + |y|\) --> if \(x=2\) and \(y=2\) then answer is NO but if \(x=1\) and \(y=0\) then answer is YES. Not sufficient.

(1)+(2) Only one solution \(x=1\) and \(y=0\). Sufficient.

Answer: C.