Hi sterling19,

While you've selected the correct answer, your logic is incomplete/incorrect.

We're told that X is a POSITIVE INTEGER.

Fact 1: X^W = 1

You correctly deduced that W could be 0 or 1, but W can actually be ANY VALUE (if X = 1, 1^(any) = 1). In that same way, X can be ANY positive integer (if X = 0, (any)^0 = 1).

Fact 1 is INSUFFICIENT

Fact 2: W is even

This tells us nothing about the value of X.

Fact 2 is INSUFFICIENT

Combined, we know....

X^W = 1

W is EVEN

IF....

W = 0, then X = ANY positive integer (1^0 = 2^0 = 3^0, = 1 etc.)

W = 2, 4, 6, 8, etc. then X = 1 (1^2 = 1^4 = 1^6 = 1^8 = 1 etc.)

W = -2, then X = 1 since (1^(-2) = 1)

So, W can be ANY EVEN INTEGER and X can be ANY positive integer.

Combined, INSUFFICIENT

Final Answer:

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Rich

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