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

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Math Expert
Joined: 02 Sep 2009
Posts: 52231
If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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20 May 2018, 23:09
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Difficulty:

35% (medium)

Question Stats:

70% (01:07) correct 30% (01:00) wrong based on 193 sessions

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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|

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Joined: 07 Dec 2017
Posts: 868
Re: If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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21 May 2018, 00:13
Bunuel wrote:

GMAT Club Tests' Fresh Question:

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

(1) |x| = |y|

(2) y = |x|

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.

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Re: If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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21 May 2018, 00:35
viveknegi wrote:
Why not A ?

Posted from my mobile device

Posted from my mobile device

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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If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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21 May 2018, 00:48
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.
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Re: If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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24 Dec 2018, 01:25
Bunuel wrote:

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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Joined: 24 Nov 2018
Posts: 75
Location: India
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Re: If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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25 Dec 2018, 23:47
Bunuel wrote:

GMAT Club Tests' Fresh Question:

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

(1) |x| = |y|

(2) y = |x|

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.
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Re: If xy ≠ 0, what is the value of x/|y| ?  [#permalink]

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28 Dec 2018, 23:33
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.

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Re: If xy ≠ 0, what is the value of x/|y| ? &nbs [#permalink] 28 Dec 2018, 23:33
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