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# Is |x|/x=1

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Math Expert
Joined: 02 Aug 2009
Posts: 5938

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25 May 2017, 10:12
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Difficulty:

45% (medium)

Question Stats:

62% (01:08) correct 38% (01:39) wrong based on 58 sessions

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Is $$\frac{|x|}{x}\neq{1}$$, where x and y are non-zero integers?

(1) $$xy=|y|x$$

(2) $$\frac{y}{x}=2$$

source - self

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Senior Manager
Joined: 24 Apr 2016
Posts: 333
Re: Is |x|/x=1 [#permalink]

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25 May 2017, 10:51
The question is basically asking whether X is negative?

Statement 1 : xy = |y|X

Here

if x is negative and y is positive, the above holds true

if x is positive and y is positive, the above hold true

Since x be positive or negative, this statement is not sufficient.

Statement 2: y/x = 2

If both x and y are positive, the above holds true and if both x and y are negative, also the above holds true.

Since x be positive or negative, this statement is not sufficient.

Combining the above two statements, we see that both statement 1 & 2 hold true only if both x and y are positive. Therefore |x|/x is equal to 1. Hence sufficient.

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Re: Is |x|/x=1 [#permalink]

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25 May 2017, 10:54
x and y are non-zero integers. |x|/x = 1 if x is positive, |x|/x = -1 if x is negative.

Statement 1. xy = |y|x
Since x is non-zero, we can cancel x from both sides.
We get y = |y| which means y is positive. But we don't know anything about x, Insufficient.

Statement 2. y = 2x, clearly insufficient to know whether x is positive or negative. Insufficient.

Combining the two statements, y is positive and x = y/2 so x is also positive. That means |x|/x = 1.
This answers with NO to the question asked. Sufficient.

Re: Is |x|/x=1   [#permalink] 25 May 2017, 10:54
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# Is |x|/x=1

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