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 \(y=0\).

SufficientStatement 2: \(y\) can take any value.

InsufficientOption \(A\)

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.