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# Is |x−5|>4?

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20 Feb 2013, 10:08
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55% (hard)

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61% (01:53) correct 39% (02:15) wrong based on 285 sessions

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Is |x−5|>4?

(1) x^2 −4>0

(2) x^2−1<0

Please elaborate the approach . I got the answer wrong and did not quite get the OE.
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Joined: 02 Sep 2009
Posts: 61302
Re: Is |x−5|>4?  [#permalink]

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20 Feb 2013, 10:37
2
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guerrero25 wrote:
Is |x−5|>4?

(1) x^2 X−4>0

(2) x^2−1<0

Please elaborate the approach . I got the answer wrong and did not quite get the OE.

m09 q19

Is $$|x-5|>4$$?

Is $$|x-5|>4$$? --> is $$x<1$$ or $$x>9$$?

(1) x^2-4>0 --> x^2>4 --> |x|>2 --> x<-2 or x>2, so we can have an YES answer as well as a NO answer (consider x=-5 and x=5). Not sufficient.

(2) x^2-1<0 --> x^2<1 --> |x|<1 --> -1<x<1. Sufficient.

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Re: Is |x−5|>4?  [#permalink]

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20 Feb 2013, 11:41
2
guerrero25 wrote:
Is |x−5|>4?

(1) x^2 −4>0

(2) x^2−1<0

Please elaborate the approach . I got the answer wrong and did not quite get the OE.

IxI > a means x > a or x<-a
keeping that in mind , solve for the stem ie Ix-5I >4
you will get x > 9 or x <1 hence the question is "Is x > 9 or x <1"

1. Solve for Statement 1: (x-2)(x+2) >0 that means the range is x>2 or X <-2 visualize this on number line you will know certainly end up eliminating Statement 1

2. Similarly solve for statement 2: (x-1)(x+1)<0
this means that -1<x<1
hence is sufficeient as the the range is less than what asked in the question....

if you are facing difficult solving inequality modulus ....i would recommend...visit the blogs of Karishma...in the below mentioned thread.....

http://www.veritasprep.com/blog/2011/01 ... edore-did/
http://www.veritasprep.com/blog/2011/01 ... h-to-mods/
http://www.veritasprep.com/blog/2011/01 ... s-part-ii/
http://www.veritasprep.com/blog/2012/07 ... -and-sets/

you will be able to solve almost all mod and inequalities questions and yes do not forget topress kudos if my post helps!!!!

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Re: Is |x−5|>4?  [#permalink]

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01 Sep 2017, 17:33
guerrero25 wrote:
Is |x−5|>4?

(1) x^2 −4>0

(2) x^2−1<0

Please elaborate the approach . I got the answer wrong and did not quite get the OE.

Stmnt 1

x^2> 4

x>2 OR x<-2

0 or -3 could satisfy the condition for example however 3 cannot not

Stmnt 2

X^2< 1

-1< x <1

Suff

B
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Re: Is |x−5|>4?  [#permalink]

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16 Sep 2017, 10:56
But doesn't x<-2 mean that x is always < 1?
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Re: Is |x−5|>4?  [#permalink]

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17 Sep 2017, 01:38
Alabama wrote:
But doesn't x<-2 mean that x is always < 1?

Yes, if x is less than -2, then it's definitely less than 1 also.
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Re: Is |x−5|>4?  [#permalink]

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17 Sep 2017, 03:55
Yes, if x is less than -2, then it's definitely less than 1 also.[/quote]

So this means statement A is also sufficient. No? One of the alternatives is sufficient as well as it is in statement B
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Re: Is |x−5|>4?  [#permalink]

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17 Sep 2017, 04:01
Alabama wrote:
Yes, if x is less than -2, then it's definitely less than 1 also.

So this means statement A is also sufficient. No? One of the alternatives is sufficient as well as it is in statement B[/quote]

The question asks is $$x<1$$ or $$x>9$$?

(1) says: x < -2 or x > 2. If x = -5, then answer is YES but if and x = 5, the answer is NO. Not sufficient.
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Re: Is |x−5|>4?  [#permalink]

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20 Jan 2020, 21:23
The answer should be E. Because we are not considering x<9. As per the question stem, we need to find whether 9<x<1 or not. As per statement B, we are getting -1<x<1. How we can say it is satisfying the answer?
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Re: Is |x−5|>4?  [#permalink]

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20 Jan 2020, 22:14
The answer should be E. Because we are not considering x<9. As per the question stem, we need to find whether 9<x<1 or not. As per statement B, we are getting -1<x<1. How we can say it is satisfying the answer?

First of all, the question asks whether $$x<1$$ or $$x>9$$.

(2) says that $$-1 < x < 1$$. So, we have a NO answer to the question. That's why it's sufficient.
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Re: Is |x−5|>4?  [#permalink]

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22 Jan 2020, 05:45
first from the given question, see in what range of numbers |x-5| > 4

we get that X>9 and X < 1 .

statement 1 says , X^2 - 1 > 0 , this means X> 2 and X < -2 , these x values doesn't come under the range of our required, so some time the answer will be yes and some times no , so insufficient

statement 2 says X^2-1 < 0 , this means x lies btw -1 and 1, this is partly included in the total range of required values so m yes

so the correct option B.
Re: Is |x−5|>4?   [#permalink] 22 Jan 2020, 05:45
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