Uri wrote:Is |x-z|>|x-y|?
1) |z|>|y|
2) 0>x

OA: [spoiler](E)[/spoiler]

What is the best way to attack this type of problem, where the absolute value is considered in both the sides? I find that picking numbers is very much time-consuming. Is there any other way out?

One thing that's important to recognize is that |k| is the distance from k to 0 on the number line.
Similarly, |x-z| gives us the distance between x and z on the number line and |x-y| gives us the distance between x and y on the number line.

So, the question can be reworded as "On the number line, is z further away from x than y is?"
From here, you can use the number line and try different values of x, y, and z to determine the answer. Using the number line approach, will give you a nice visual to work with.