GMAT Club Tests' Fresh Question:

If xy ≠ 0, what is the value of x/|y| ?


(1) |x| = |y|

(2) y = |x|
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Hi,

Because (1) isn't enough...
Try using x = 1 and y = 1. Then |x|=|y|=1 as required by (1) and x/|y| = 1/1 = 1.
Next use x = -1 and y = 1. Then |x|=|y|=1 as required by (1) but x/|y| = -1/1 = -1.

We have two different pairs of (x,y) that fulfill the criteria of (1) but give different values for x/|y|.
Insufficient.
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Par of GMAT CLUB'S New Year's Quantitative Challenge Set

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From the question stem, we know that x and y can take any values except 0. Additionally, the sign that the expression \(x/|y|\) takes will depend on x since |y| is always positive. With these observations in mind, lets move to statements.

Statement 1: We can deduce that the expression \(x/|y|\) will always be 1 or -1. Sign depends on value of x, like we have observed earlier. Hence, insufficient

Statement 2: Again, using this statement, the expression \(x/|y|\) gives us two values 1 and -1 because numeric values of x and y cancel each other and sign depends on x. Hence, insufficient

Combining statements 1 & 2: We can still not come up with a unique value for the expression \(x/|y|\). The only thing we get is that y is intrinsically a positive number.

Hence, answer is E
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