Hi sakshi7591,

What is the source of this question? I ask because it appears to be a GRE prompt (so it really shouldn't be posted on this site - as this type of prompt won't appear on the GMAT). That having been said, you can solve it by TESTing VALUES, but you'll have to consider a number of different possibilities.

Here's an example to get you started...

We're told that |X| < |Y+2| < |Z| AND that Y>0 and XZ> 0. We're clearly meant to consider NEGATIVE values for X and Z at some point, but I'm going to start with an obvious example first.

IF....
X=1, Y=2, Z=5
then Answer B is true.

Staying with this example, and looking at the other answer choices, does Y have to be greater than X? Do they have to be integers? Can you come up with another example using all positive numbers that would confirm one (or more) of the remaining answers? Now how about if X and Z are NEGATIVE?

With a little bit of 'playing around' and some basic arithmetic, you should be able to find all of the answers that COULD be true.

GMAT assassins aren't born, they're made,
Rich

Hi sakshi7591,

To start, you have to recognize that XZ > 0 means that X and Z could both be NEGATIVE. Once you realize that, and you prove that Answer B could be true, then you can just turn the X and Z into negatives...

IF....
X= -1, Y=2, Z= -5
then Answer E is true.

GMAT assassins aren't born, they're made,
Rich