Is (x + 1)/(x - 3) < 0 ?

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Is (x + 1)/(x - 3) < 0 ? [#permalink]

11 Feb 2011, 02:57

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67% (01:59) correct

32% (00:41) wrong

based on 5 sessions

Is (x + 1)/(x - 3) < 0 ?

(1) -1 < x < 1
(2) x^2 - 4 < 0

[Reveal] Spoiler: OA

Last edited by Bunuel on 10 May 2013, 01:23, edited 1 time in total.

Edited the question.

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Re: data suff inequalities [#permalink]

11 Feb 2011, 05:30

Let p=(x+1)/(x-3)<0

Statement 1:
-1<x<1
So Range of p is between 0 and -1
Therefore, p is less than 0.
Sufficient.

Statement 2:
x^2-4 < 0
x^2 < 4
Take sq. rt. on both sides:
|x| < 2

=> -2<x<2
1/5<p<-3 [Range]
So we cannot say if p is less than 0
In Sufficient!

Ans A
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Re: data suff inequalities [#permalink]

11 Feb 2011, 07:44

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Lolaergasheva wrote:

Is x+1/x-3<0 ?

1) -1 < x < 1
2) x^2-4 < 0

Lolaergasheva, please format the questions properly:

Question should read:

Is (x+1)/(x-3)<0 ?

Is \frac{x+1}{x-3}<0? --> roots are -1 and 3, so 3 ranges: x<-1, -1<x<3 and x>3 --> check extreme value: if x some very large number then \frac{x+1}{x-3}=\frac{positive}{positive}>0 --> in the 3rd range expression is positive, then in 2nd it'll be negative and in 1st it'll be positive again: + - +. So, the range when the expression is negative is: -1<x<3.

Thus the question basically becomes: is -1<x<3?

(1) -1 < x < 1. Sufficient.
(2) x^2-4 < 0 --> -2<x<2. Not sufficient.

Answer: A.

Check for more about the approach used here: everything-is-less-than-zero-108884.html?hilit=extreme#p868863, here: inequalities-trick-91482.html and here: xy-plane-71492.html?hilit=solving%20quadratic#p841486

And again:

!	Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.

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Re: data suff inequalities [#permalink]

17 Mar 2011, 22:19

Another easy way to solve this problem...
1) -1<x<1
Plug in 1/2 and -1/2 in original statement, you will see that it is always negative.
2)-2<x<2
-3/2 gives you a positive value...hence not sufficient.

A

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Re: data suff inequalities [#permalink]

04 Aug 2011, 00:24

picking numbers here was short and precise:

S2-start with 1.5 (the answer is yes) and -1.5 (the answer is no). SO NS
S1- 0.5 AND -0.5 the answer is yes in both.though, picking numbers in is risky.

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Re: data suff inequalities [#permalink]

07 Aug 2011, 03:59

Bunuel, thanks for the explanation. +1+1
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Re: Is x+1/x-3<0 ? 1) -1 < x < 1 2) x^2-4 < 0 [#permalink]

10 Jan 2012, 14:50

This one's a thing of beauty.

NOTE: No property mentioned about x, so can't cross-multiply the inequality.
RULE1: If positive, cross-mutiply sign does not change
RULE2: If negative, cross-mutiply sign changes

1. This means that x is + or - fraction. Substituting gives us that the inequality will hold true for all fractions of x, both + or -. Suff.
2. x^2 - 4 < 0 => x^2 < 4 => x < 2 or x > -2. If x = 1.5, inequality holds true. If x = -1.5, it does not. Insuff.

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Re: Is x+1/x-3<0 ? 1) -1 < x < 1 2) x^2-4 < 0 [#permalink] 10 Jan 2012, 14:50

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