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

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

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Math Expert

Joined: 02 Sep 2009

Posts: 55277

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

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03 Aug 2018, 05:26

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Difficulty:

25% (medium)

Question Stats:

66% (01:09) correct

34% (01:14) wrong

based on 529 sessions

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If \(y ≠ 0\), is \(|x| = 1\) ?

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

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

NEW question from GMAT® Quantitative Review 2019

(DS05986)

Spoiler: OA

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Intern

Joined: 03 Apr 2018

Posts: 7

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

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03 Aug 2018, 05:42

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.

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

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03 Aug 2018, 05:44

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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19 Oct 2018, 09:57

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