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

Question

GMAT Club Tests' Fresh Question:

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

(1) |x| = |y|

(2) y = |x|

M36-47

Bunuel · Accepted Answer

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

DavidTutorexamPAL · Answer

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.

DavidTutorexamPAL · Answer

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.

US09 · Answer

The question asks to check whether  x is +ve or -ve  given that x & y are not 0.

1) |x|=|y|. So, the absolute value of x is equal to that of y. That means if x=-1, y can be -1/1, x=1, y can again be -1/1; Similarly if x=-2, y can be 2,-2., x=2, y can again be -2/2. Gives no idea about the definite sign of x.  Not Sufficient.

2) y=|x|. So, if x=-1, y=1; if x=1, y =1. Again checking for the sign of x, both +ve and -ve are possible.  Not Sufficient.

Combining 1 & 2, again x can have both +ve and -ve values.  Insufficient . Hence, E.

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Ypsychotic · Answer

Statement 1) If x=+/-y. Expression can be +1 or -1. Insufficient.

Statement 2) y=|x|, Expression =x/|x|, would be +1 for positive value of x. -1 for negative value of x. INsufficient.

(1)+(2), INsufficient.

Option E is correct.

GMATin · Answer

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

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