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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