Hi All,

This DS question can be solved with a mix of Number Property Rules and TESTing VALUES:

We're told that X cannot = 0. We're asked for the value of [(X^W)/(X^Y)]^4

While this may look "scary", it's actually based on some basic math rules/patterns. Notice how the "base" of both the numerator AND the denominator are the SAME....that matters....

Fact 1: W = Y

Let's TEST VALUES:

IF...

X = 1

W = 1

Y = 1

[(1^1)/(1^1)]^4 = (1/1)^4 = 1

IF....

X = 2

W = 3

Y = 3

[(2^3)/(2^3)]^4 = (8/8)^4 = (1/1)^4 = 1

From this work, you should notice that the fraction ALWAYS equals 1, so the answer will ALWAYS be 1^4 = 1. That will always occur regardless of what you TEST for the 3 variables (in Fact 1).

Fact 1 is SUFFICIENT

Fact 2: X^2 = 1

This tells us that X = 1 OR X = -1

Here's where some Number Property knowledge comes in handy.

+1 raised to ANY power = 1, so (1^W) and (1^Y) BOTH always = 1......and 1/1 = 1.....so 1^4 = 1

-1 raised to an EVEN power = 1

-1 raised to an ODD power = -1

While this might appear to yield different answer, you must remember what the specific question asks for....

With these two restrictions on the numerator and denominator, we have 4 possible calculations (and 2 possible outcomes):

(+1)/(-1) = -1

(-1)/(+1) = -1

(+1)/(+1) = 1

(-1)/(-1) = 1

(-1)^4 = 1

(+1)^4 = 1

So the answer is the SAME regardless.

Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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