Hi All,
When complex-looking questions show up on Test Day, there's almost always some type of built-in pattern involved. If you can't immediate spot the pattern, then you have to put in a bit of work to prove what the pattern actually is....TESTing VALUES can help you to prove that a pattern exists.....
Here, we're told that Y >= 0. We're asked for the value of X.
Fact 1: |X-3| >= Y
IF....
Y = 0
Then |X-3| >= 0, so X can be ANY number. As Y gets bigger, certain options are eliminated, but given this 'restriction', X has an infinite number of possibilities.
Fact 1 is INSUFFICIENT
Fact 2: |X-3| <= -Y
Here, we have to be CAREFUL with the details. Notice how there's a NEGATIVE sign in front of the Y.....
IF....
Y = 0
|X-3| <= 0
Absolute values CANNOT have negative results - the result is ALWAYS 0 or a positive, so this TEST has JUST ONE solution...
X = 3
IF....
Y = 1
|X-3| <= - 1 which is NOT POSSIBLE.
From the prompt, we know that Y >= 0, so choosing a positive value for Y will NOT fit the absolute value given in Fact 2. This means that the ONLY possible value for Y is 0. By extension, there is ONLY ONE possible value for X....X = 3.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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