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If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x

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Math Expert
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Joined: 02 Sep 2009
Posts: 51167
If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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New post 03 Aug 2018, 04:26
1
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A
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D
E

Difficulty:

  35% (medium)

Question Stats:

64% (00:54) correct 36% (00:58) wrong based on 351 sessions

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Posts: 7
Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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New post 03 Aug 2018, 04:42
A.

(1) If \(y > 0\), then \(x = 1\) [ positive number divided by its absolute value is 1 ]
If \(y < 0\), then \(x = -1\) [ negative number divided by its absolute value is -1 ]
In both cases, value of \(x\) is either 1 or -1, so \(|x| = 1\). SUFFICIENT.

(2) \(|x| = -x\)
This is true for all x less than or equal to 0. NOT SUFFICIENT.
Director
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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New post 03 Aug 2018, 04:44
Bunuel wrote:
If \(y ≠ 0\), is \(|x| = 1\) ?


(1) \(x = \frac{y}{|y|}\)

(2) \(|x| = -x\)


NEW question from GMAT® Quantitative Review 2019


(DS05986)


Question stem, is \(|x| = 1\) ?

St1:- \(x = \frac{y}{|y|}\)
When y>0, \(x = \frac{y}{y}\) (where y is non-negative and non-zero)
Or, x=1; so |x|=1

when y<0, \(x = \frac{y}{-y}\)
Or, x=-1; so |x|=1
Sufficient.

St2:- \(|x| = -x\)
Or, \(|x|+x=0\)
Or, \(x\leq0\)
Insufficient.

Ans. (A)
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Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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New post 19 Oct 2018, 08:57
Bunuel wrote:
If \(y ≠ 0\), is \(|x| = 1\) ?


(1) \(x = \frac{y}{|y|}\)

(2) \(|x| = -x\)


NEW question from GMAT® Quantitative Review 2019


(DS05986)


From statement 1) x |y| = y

the only possible way for both sides to be equal if x = 0 or 1 or -1, however y cannot be zero.

so x is 1 or -1, sufficient.

From statement 2) |x| = -x

x can be 0 or -1

Two different answers.

Insufficient.

Answer choice A
GMAT Club Bot
Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x &nbs [#permalink] 19 Oct 2018, 08:57
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