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:
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Rich
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