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# What is the smallest integer that satisfies the inequality ? (x - 3)/

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
What is the smallest integer that satisfies the inequality ? (x - 3)/  [#permalink]

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13 Mar 2016, 08:48
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:34) correct 36% (01:50) wrong based on 133 sessions

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What is the smallest integer that satisfies the inequality $$\frac{(x - 3)}{(x^2 - 8x - 20)} > 0$$ ?

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

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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: What is the smallest integer that satisfies the inequality ? (x - 3)/  [#permalink]

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14 Mar 2016, 01:00
Bunuel wrote:
What is the smallest integer that satisfies the inequality $$\frac{(x - 3)}{(x^2 - 8x - 20)} > 0$$ ?

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

Hi,

WHAT is the info?

$$\frac{(x - 3)}{(x^2 - 8x - 20)} > 0$$ ..
means both x-3 amd x^2-8x-20 should be of the same sign and should not be equal to 0..

method-1

First method would be substitute the choices given..
Since we are looking for MINIMUM integer, start from the lowest..
-2 will give you undefined number -5/0..OUT
-1 gives you -4/-11=4/11.. CORRECT

Method-2

$$\frac{(x - 3)}{(x^2 - 8x - 20)} > 0$$=$$\frac{(x - 3)}{(x^2 - 10x+2x - 20)} > 0$$
=> $$\frac{(x - 3)}{(x - 10)(x+2)} > 0$$...
so at 3, the equation will become 0..
and at x=-2 and x=10, solution is undefined..
Amongst choices ONLY 0 and -1 are left..
-1 will make numerator (x-3) as -ive and denominator(x - 10)(x+2) also as -ive..
so -1 is CORRECT..
D

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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GMAT 1: 660 Q48 V31
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Re: What is the smallest integer that satisfies the inequality ? (x - 3)/  [#permalink]

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30 Apr 2016, 11:28
We can solve by pluggin the answers in the given equation.

Since we need to find the smallest integer, we will start with pluggin the value x = -2
(2-3)/(4+16-20) which is not right ..Eliminate

Put value x = -1
(-1-3)/(1+8-20) = -4/-11

Ans: D
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Re: What is the smallest integer that satisfies the inequality ? (x - 3)/  [#permalink]

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15 Oct 2018, 02:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the smallest integer that satisfies the inequality ? (x - 3)/   [#permalink] 15 Oct 2018, 02:47
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