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.

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jeevan ki katha says

It should be Option 4.

I tried with 0 and that gave me 3/20, which is positive, so, I skipped 10 and 3 (options 2 and 3), tried it with -1 and got a 4/11 (positive), tried it with -2 and got-5/0 , so… -1 is the lowest integer that satisfies it.

Let me know if I am right or wrong.

4GMAT - GMAT Classes, Math eBooks says

Your answer is absolutely correct. -1 is the smallest integer that will satisfy this condition