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# If у + |y| = 0, which of the following must be true?

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Manager
Joined: 10 Feb 2011
Posts: 107
If у + |y| = 0, which of the following must be true?  [#permalink]

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18 Feb 2011, 10:16
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35% (medium)

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55% (00:42) correct 45% (00:41) wrong based on 1304 sessions

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If у + |y| = 0, which of the following must be true?

(A) у > 0
(B) у is no less than 0
(C) у < 0
(D) у is not greater than 0
(E) y = 0
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Math Expert
Joined: 02 Sep 2009
Posts: 53831
Re: If у + y = 0, which of the following must be true? (  [#permalink]

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18 Feb 2011, 10:30
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banksy wrote:
199. If у + IyI = 0, which of the following must be true?
(A) у > 0
(B) у is no less than 0
(C) у < 0
(D) у is not greater than 0
(E) y = 0

$$y+|y| = 0$$ --> $$|y|=-y$$. Now, LHS is an absolute value which is never negative hence RHS must also be non-negative: $$-y\geq{0}$$ --> $$y\leq{0}$$.

Or you can see right away that in order $$y+|y|=0$$ to hold true y must be either negative number (for example -3+|-3|=0) or zero (0+|0|=0).

Answer: D.
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Intern
Joined: 01 Sep 2016
Posts: 28
Re: If у + |y| = 0, which of the following must be true?  [#permalink]

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06 Sep 2016, 00:25
whts the difference between option c and d
Intern
Joined: 08 Sep 2016
Posts: 2
Location: United States
GMAT 1: 700 Q49 V37
GPA: 3.44
Re: If у + |y| = 0, which of the following must be true?  [#permalink]

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11 Sep 2016, 10:52
1
sanaexam wrote:
whts the difference between option c and d

The difference is that C just implies that Y <0, where as D says Y < 0 or Y = 0.

If you plug values in as Y = 0, it will satisfy the equation.
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Posts: 10207
Re: If у + |y| = 0, which of the following must be true?  [#permalink]

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21 Dec 2018, 09:26
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Re: If у + |y| = 0, which of the following must be true?   [#permalink] 21 Dec 2018, 09:26
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# If у + |y| = 0, which of the following must be true?

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