Data Sufficiency

Vincen wrote:Is |x| < 5?

(1) x^2 < 16

(2) x(x - 5) < 0

The OA is D.

Clearly Statement (1) is sufficient. But, why statement (2) is sufficient?

Let's look at x(x - 5) < 0.

To make x(x - 5) < 0, you must not assume that x is negative, else x as well as (x - 5) would be negative, making x(x - 5) positive.

So, x cannot be negative.

x cannot be either 0 or 5, else x(x - 5) would be 0.

x cannot be greater than 5. For example, say x = 6.

Then, x(x - 5) < 0 => 6*(6 - 5) < 0 => 1 not less than 0.

Thus, 0 < x < 5. Thus, |x| < 5. Sufficient.

The correct answer: D

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Hyderabad | Mexico City | Toronto | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.