GMAT Inequalities – Least integer

Here is an interesting inequalities question.

What is the smallest integer that satisfies the inequality ?
(x – 3)/ (x^2 – 8x – 20) > 0

A. -2
B. 10
C. 3
D. -1
E. 0

Correct Answer : -1. Choice D

Let us factorize the denominator and rewrite the expression as (x – 3) / {(x – 10)(x + 2)}
The values of x that are of interest to us are x = 3, x = 10 and x = -2.

Let us arrange them in ascending order. -2, 3 and 10.

The quickest way to solve inequalities questions after arriving at these values is verifying if the inequality holds good at these intervals.

Interval 1 : x <  -2.  Let us take x = -10. When x = -10, (x – 3)/ (x^2 – 8x – 20) < 0; the inequality does not hold good in this interval.

Interval 2: -2 < x < 3. Let us take x = -1. When x = -1, (x – 3)/ (x^2 – 8x – 20) > 0; the inequality holds good in this interval.

The least integer value that x can take if x > -2 is x = -1. So, the correct answer is -1. Choice D.

Note : In any inequality question, when the interval in which the inequality holds good is determined, we have to watch out to eliminate values of x for which the denominator will become zero.

You could access additional GMAT inequality practice questions by clicking here.