Ian Stewart wrote:Almost every difficult absolute value question on the GMAT is testing whether you understand that absolute value measures distance:

|c| is the distance, on the number line, from c to zero;
|c - d| is the distance, on the number line, between c and d.

The question tells us a < y < z < b. We know a is furthest to the left on the number line, b furthest to the right, and y is closer to a than z is. We can draw the points on the number line. The question asks:

Is |y - a| < |y - b|?

In words, using the distance interpretation above, this just asks "Is the distance between y and a less than the distance between y and b?" In other words, "Is y closer to a than it is to b?"

1) tells us that z is closer to a than to b. Well, y is even closer to a than z is, so y must be closer to a than to b. Sufficient.

2) tells us that y is closer to a than z is to b. Well, y is even further away from b than z is, so y must be closer to a than to b. Sufficient.

D.

It's a lot easier if you draw the number line and think about what the distance statements are telling you while looking at the picture.

Vignesh.4384 wrote:Hi Ian,

As per your explanation .. i consider 4 point on the number line

a = -4
y = 1
z = 2
b = 3

This follows the rule a < y < z < b.

Here if u notice the distance between y and a is greater than y and b right ?

Could you please explain this ?