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Bunuel
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What is the value of y? 03 Dec 2017, 00:50
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47% (01:23) correct 53% (01:36) wrong based on 179 sessions

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What is the value of y?


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

(2) \(|y| \geq x \geq -|y|\)
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niks18
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What is the value of y? 03 Dec 2017, 03:47
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Bunuel
What is the value of y?


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

(2) \(|y| \geq x \geq -|y|\)
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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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What is the value of y? 04 Dec 2017, 01:55
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niks18
Bunuel
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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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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What is the value of y? 04 Dec 2017, 02:16
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niks18
Bunuel
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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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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What is the value of y? 04 Dec 2017, 02:20
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Got it. I didn't look into the inequality signs closely enough. My bad. Thanks!

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What is the value of y? 22 Apr 2021, 10:24
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