vitorpteixeira wrote:

If |2x| > |3y|, is x > y?

(1) x > 0

(2) y > 0

Inequalities + absolute values + Data Sufficiency makes this a good problem to use a number line.

Start by understanding the question itself. On a number line, |2x| > |3y| means that 2x is further from the origin than 3y.

'is x > y' means that we want to know whether x is to the right of y, or to the left of y. If we're testing cases, we'll be trying to find a case where x is to the left, and another case where x is to the right. That's the only way we can prove insufficiency.

Statement 1:

x > 0 means that x must be to the right of 0.

So, 2x must be to the right of 0.

From the question stem, we know that 3y must be closer to the origin than 2x is.

However, 3y could be on either side of the origin, as long as it's closer.

It could be on the left, in which case the situation looks like this:

Or it could be on the right, in which case the situation looks like this:

Either way, y is definitely to the left of x. So the answer to the question is 'yes', and this statement is sufficient.

Statement 2:

This time, we know that y is to the right of the origin. 3y will also be to the right of the origin, like this:

2x could be to the left of the origin, like this:

It could also be to the right of the origin, like this. It does have to be closer to the origin than 3y, but let's take it to an extreme. Let's make 2x just a tiny bit closer than 3y.

We've drawn one picture with x to the left of y, and another picture with x to the right. Since the result can go either way, statement 2 is insufficient.

The answer is A.

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