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

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

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New post 13 Mar 2016, 09:48
1
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:36) correct 38% (01:47) wrong based on 149 sessions

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

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New post 14 Mar 2016, 02:00
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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Re: What is the smallest integer that satisfies the inequality ? (x - 3)/  [#permalink]

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New post 30 Apr 2016, 12:28
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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New post 15 Oct 2018, 03:47
Hello from the GMAT Club BumpBot!

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Re: What is the smallest integer that satisfies the inequality ? (x - 3)/   [#permalink] 15 Oct 2018, 03:47
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