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21 May 2018, 00:09
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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GMAT Club Tests' Fresh Question:
If xy ≠ 0, what is the value of x/|y| ?
(1) |x| = |y|
(2) y = |x|
M36-47
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08 Nov 2021, 02:51
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Bunuel
Official Solution:
If \(xy ≠ 0\), what is the value of \(\frac{x}{|y|}\) ?
(1) \(|x| = |y|\)
The above means that \(x\) and \(y\) have the same magnitude but we don't know the sign of \(x\) to determine the value of \(\frac{x}{|y|}\). If \(x < 0\), then \(\frac{x}{|y|}=-1\) (for example, consider \(x=-1\) and \(y=1\)) but if \(x > 0\), then \(\frac{x}{|y|}=1\) (for example, consider \(x=1\) and \(y=1\)). Not sufficient.
(2) \(y = |x|\)
The above means that \(y > 0\) (it equals to the absolute value of non-negative number \(x\)) but again we don't know the sign of \(x\). If \(x < 0\), then \(\frac{x}{|y|}=-1\) (for example, consider \(x=-1\) and \(y=1\)) but if \(x > 0\), then \(\frac{x}{|y|}=1\) (for example, consider \(x=1\) and \(y=1\)). Not sufficient.
(1)+(2) We know that \(x\) and \(y\) have the same magnitude and that \(y > 0\). Still nothing about the sign of \(x\). Not sufficient.
Answer: E
General Discussion
21 May 2018, 01:13
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Bunuel
As it isn't entirely clear how to start, we'll use simple numbers to find contradictory examples.
This is an Alternative approach.
(1) Say that x = 1. Then y =1 or y = -1. In both cases x/|y| = 1/1 = 1. Let's try to contradict this. Say that x is negative, that is x = -1. In this case y could still be 1 or -1 and x/|y| = -1. As we have two different answers, this is not enough.
Insufficient.
(2) Say that x = 1. Then y = 1 and x/|y| = 1. Say that x = -1. Then y = 1 and x/|y| = -1/1 = -1.
Also insufficient.
Combined.
Both of our examples (x = 1, y =1 and x = -1, y = 1) work in both statements and give different answers.
Insufficient.
(E) is our answer.
