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# For which of the following inequalities is x^2 - 2<-1

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Intern
Joined: 26 Jun 2014
Posts: 6
For which of the following inequalities is x^2 - 2<-1  [#permalink]

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Updated on: 18 Jul 2014, 07:15
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15% (low)

Question Stats:

78% (01:03) correct 22% (01:05) wrong based on 121 sessions

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For which of the following inequalities is x^2 - 2 < -1 ?

A. x<1
B. x<-1
C. x<0
D. -1<x<1
E. x<-1 or x>1

I solved the equation as
=> x^2 - 2 +1 <0
=> x^2 -1 <0
=> (x+1)(x-1) < 0
x+1 < 0 or x-1<0
x< -1 or x < 1

I am not sure what am I doing wrong

Originally posted by ashutoshbarawkar on 17 Jul 2014, 19:49.
Last edited by Bunuel on 18 Jul 2014, 07:15, edited 2 times in total.
Edited the question.
Director
Joined: 25 Apr 2012
Posts: 636
Location: India
GPA: 3.21
Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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17 Jul 2014, 20:05
1
ashutoshbarawkar wrote:
For which of the following inequalities is x^2 - 2<-1
a. x<1
b. x<-1
c. x<0
d. -1<x<1
e. x<-1 or x>1

I solved the equation as
=> x^2 - 2 +1 <0
=> x^2 -1 <0
=> (x+1)(x-1) < 0
x+1 < 0 or x-1<0
x< -1 or x < 1

I am not sure what am I doing wrong

Hello Ashutosh,

The given equation can be written as$$x^2< 1$$

Now since $$x^2\geq{0}$$ therefore both LHS and RHS are non-negative

So taking squareroot we get

$$\sqrt{x^2} <1$$

Important Property of Mod $$\sqrt{x^2} =|x|$$

So we have |x|< 1 or -1<x<1

Ans is D.

The question can also be done using graphical approach. Check out the below link for a similar problem.

if-x-is-an-integer-what-is-the-value-of-x-1-x-2-4x-94661.html

Have a look at the below links for easy navigation on Gmatclub

all-you-need-for-quant-140445.html#p1130136
new-to-the-gmat-club-start-here-130870.html
gmat-prep-software-analysis-and-what-if-scenarios-146146.html

ATB
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Intern
Joined: 26 Jun 2014
Posts: 6
Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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17 Jul 2014, 21:01
Thanks for the explanation.

I am still confused about why the method I am using is wrong.

(x-1)(x+1)<0
x-1<0 or x+1<0
x<1 or x<-1
Director
Joined: 25 Apr 2012
Posts: 636
Location: India
GPA: 3.21
Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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17 Jul 2014, 23:06
ashutoshbarawkar wrote:
Thanks for the explanation.

I am still confused about why the method I am using is wrong.

(x-1)(x+1)<0
x-1<0 or x+1<0
x<1 or x<-1

Okay...If you look at the graphical method you can understand better..Having said that let's test some values

We have (x-1)(x+1)<0
So x=-1 and x=1

Now Let's take x=2 and see what happens to the expression
We get (2-1)(2+1)<0 or 3<0 which is incorrect.

So we need to identify a region where the above equation holds good.
Consider x=0, the expression is -1<0 Yes.

Consider x=-2, the expression is (-2-1)(-2+1) <0 or 3<0. No

Thus the only range where the equations holds good is -1<x<1...

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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
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Joined: 24 Jun 2016
Posts: 344
GMAT 1: 770 Q60 V60
GPA: 4
Re: For which of the following inequalities is x^2 - 2<-1  [#permalink]

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25 Jun 2016, 23:53
$$x^2 - 2 < -1$$ when $$x^2 - 1 < 0$$; in other words, $$(x-1)*(x+1) < 0$$

So x-1 has to be smaller than 0 and x+1 has to be greater than 0. In other words, $$-1<x<1$$

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Re: For which of the following inequalities is x^2 - 2<-1   [#permalink] 25 Jun 2016, 23:53