Bunuel wrote:
If \(y ≠ 0\), is \(|x| = 1\) ?
(1) \(x = \frac{y}{|y|}\)
(2) \(|x| = -x\)
(DS05986)
Target question: Is |x| = 1? Statement 1: \(x = \frac{y}{|y|}\) First recognize that
|y| must positive.
With this in mind let's consider two possible cases: y is positive and y is negative.
Case a: If y is negative, then x = \(\frac{y}{|y|}\) = (negative y)/(positive y) = -1, in which case |x| = |-1| = 1. So, the answer to the target question is
YES, |x| = 1Case b: If y is positive, then x = \(\frac{y}{|y|}\) = (positive y)/(positive y) = 1, in which case |x| = |1| = 1. So, the answer to the target question is
YES, |x| = 1Since both possible cases yield the same answer to the
target question, statement 1 is SUFFICIENT
Statement 2: |x| = -xThere are infinitely many values of x that satisfy the equation |x| = -x
Here are two:
Case a: x = -1 (notice that |x| = -x becomes |-1| = -(-1), which simplifies to be |-1| = 1 (which is true). In this case, the answer to the target question is
YES, |x| = 1Case b: x = -2 (notice that |x| = -x becomes |-2| = -(-2), which simplifies to be |-2| = 2 (which is true). In this case, the answer to the target question is
NO, |x| does not equal 1Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
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