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What is the value of y?

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What is the value of y? [#permalink]

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New post 02 Dec 2017, 23:50
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49% (00:50) correct 51% (01:20) wrong based on 51 sessions

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What is the value of y? [#permalink]

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New post 03 Dec 2017, 02:47
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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 \(A\)

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Re: What is the value of y? [#permalink]

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New post 04 Dec 2017, 00:55
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

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Re: What is the value of y? [#permalink]

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New post 04 Dec 2017, 01:16
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.

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Re: What is the value of y? [#permalink]

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New post 04 Dec 2017, 01:20
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, 01:20
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