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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: 51167
If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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03 Aug 2018, 04:26
1
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Difficulty:

35% (medium)

Question Stats:

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

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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, 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
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If y ≠ 0, is |x| = 1 ? (1) x = y/|y| (2) |x| = -x  [#permalink]

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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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Joined: 19 Oct 2013
Posts: 509
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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, 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

Insufficient.

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

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