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Is |x| < 5?

This topic has 1 expert reply and 0 member replies

Is |x| < 5?

Post Sun Sep 24, 2017 6:48 am
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?

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Post Sun Sep 24, 2017 9:13 pm
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!

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