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# What is the value of y?

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Math Expert
Joined: 02 Sep 2009
Posts: 44400
What is the value of y? [#permalink]

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03 Dec 2017, 00:50
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55% (hard)

Question Stats:

54% (01:16) correct 46% (01:23) wrong based on 81 sessions

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What is the value of y?

(1) $$|x| \leq y \leq -|x|$$

(2) $$|y| \geq x \geq -|y|$$
[Reveal] Spoiler: OA

_________________
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1008
Location: India
GPA: 3.82
What is the value of y? [#permalink]

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03 Dec 2017, 03:47
1
KUDOS
Bunuel wrote:
What is the value of y?

(1) $$|x| \leq y \leq -|x|$$

(2) $$|y| \geq x \geq -|y|$$

Statement 1: Mod is always positive. So for $$y≥|x |=> y≥0$$

and for $$y≤-|x| => y≤0$$. so only possible value is $$y=0$$. Sufficient

Statement 2: $$y$$ can take any value. Insufficient

Option $$A$$
Intern
Joined: 15 Oct 2017
Posts: 16
GMAT 1: 630 Q39 V38
Re: What is the value of y? [#permalink]

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04 Dec 2017, 01:55
niks18 wrote:
Bunuel wrote:
What is the value of y?

(1) $$|x| \leq y \leq -|x|$$

(2) $$|y| \geq x \geq -|y|$$

Statement 1: Mod is always positive. So for $$y≥|x |=> y≥0$$

and for $$y≤-|x| => y≤0$$. so only possible value is $$y=0$$. Sufficient

Statement 2: $$y$$ can take any value. Insufficient

Option $$A$$

I don't know if your reasoning for statement 1 being possible is correct. It would've been right if the equation was y≤|-x| but since y≤-|x|, x can also take any value in this equation. So, this is insufficient as well since there's no unique value.

Please correct me if I'm wrong
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 899
Location: India
Re: What is the value of y? [#permalink]

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04 Dec 2017, 02:16
strawhat316 wrote:
niks18 wrote:
Bunuel wrote:
What is the value of y?

(1) $$|x| \leq y \leq -|x|$$

(2) $$|y| \geq x \geq -|y|$$

Statement 1: Mod is always positive. So for $$y≥|x |=> y≥0$$

and for $$y≤-|x| => y≤0$$. so only possible value is $$y=0$$. Sufficient

Statement 2: $$y$$ can take any value. Insufficient

Option $$A$$

I don't know if your reasoning for statement 1 being possible is correct. It would've been right if the equation was y≤|-x| but since y≤-|x|, x can also take any value in this equation. So, this is insufficient as well since there's no unique value.

Please correct me if I'm wrong

Hi

The first statement goes like this:
|x|≤y≤−|x|
So its not just that y≤−|x|, but we also have |x|≤y. Now |x| can never be negative, it will be either 0 or positive. So when we have |x|≤y, then y will also be either 0 or positive. But going by y≤−|x|, y will be either 0 or negative (because |x| is either 0 or positive, and -|x| will thus be either 0 or negative).
Now combining these two pieces of information together from this statement only: y is either 0 or positive, and y is either 0 or negative. This tells us that y can only be 0. And x will also be 0, thats the only case possible.
Intern
Joined: 15 Oct 2017
Posts: 16
GMAT 1: 630 Q39 V38
Re: What is the value of y? [#permalink]

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04 Dec 2017, 02:20
Got it. I didn't look into the inequality signs closely enough. My bad. Thanks!

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Re: What is the value of y?   [#permalink] 04 Dec 2017, 02:20
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