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Is |x - 6| > 2?

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Is |x - 6| > 2? [#permalink]

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Question Stats:

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Is |x - 6| > 2?
Statement #1: |x - 4| > 3
Statement #2: |x - 8| > 1


For a discussion of inequalities and DS questions, as well as an efficient solution for this particular problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... qualities/
[Reveal] Spoiler: OA

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Re: Is |x - 6| > 2? [#permalink]

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New post 24 Oct 2013, 20:05
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Is |x - 6| > 2?
Statement #1: |x - 4| > 3
Statement #2: |x - 8| > 1

the question statement : X-6>2 and X-6<-2 ==> X>8 and X<4

Statement #1 : X-4>3 and X-4<-3 ===> x>7 and X<1
Statement #2: X-8>1 and X-8<-1 ==> X>9 and X<7

So combining 1 and 2 we get answer as X>9 and X<1 for this the question statement holds true.

So C is the answer.

+1Kudos if you like

Thanks
AB
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+1 Kudos if you like and understand.

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Re: Is |x - 6| > 2? [#permalink]

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New post 25 Oct 2013, 05:50
Bump!!! I am not able to understand the above solution , can someone illustrate??

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Re: Is |x - 6| > 2? [#permalink]

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New post 25 Oct 2013, 07:18
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Is |x - 6| > 2? What this question is basically asking us is if x > 8 or if x < 4 since any value between 4 and 8 would make the inequality not hold (try it: x = 5 |5-6| = |-1| = 1 < 2)

Statement #1: |x - 4| > 3 tells us that x > 7 or x < 1, not enough info to say whether x > 8 (could be 7.2 for example) not sufficient.
Statement #2: |x - 8| > 1 tells us that x > 9 or x < 7, not enough info to say whether x < 4, not sufficient

Taken together (1) & (2) x < 1 and x > 9: any value of x will make the inequality true so yes |x - 6| > 2. Sufficient

Answer: C

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Re: Is |x - 6| > 2? [#permalink]

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New post 25 Oct 2013, 07:30
Spunkerspawn wrote:
Is |x - 6| > 2? What this question is basically asking us is if x > 8 or if x < 4 since any value between 4 and 8 would make the inequality not hold (try it: x = 5 |5-6| = |-1| = 1 < 2)

Statement #1: |x - 4| > 3 tells us that x > 7 or x < 1, not enough info to say whether x > 8 (could be 7.2 for example) not sufficient.
Statement #2: |x - 8| > 1 tells us that x > 9 or x < 7, not enough info to say whether x < 4, not sufficient

Taken together (1) & (2) x < 1 and x > 9: any value of x will make the inequality true so yes |x - 6| > 2. Sufficient

Answer: C

This has made it super clear!! Thanks a lot!!

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Re: Is |x - 6| > 2? [#permalink]

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New post 07 Aug 2014, 21:59
bhatiamanu05 wrote:
Is |x - 6| > 2?
Statement #1: |x - 4| > 3
Statement #2: |x - 8| > 1

the question statement : X-6>2 and X-6<-2 ==> X>8 and X<4

Statement #1 : X-4>3 and X-4<-3 ===> x>7 and X<1
Statement #2: X-8>1 and X-8<-1 ==> X>9 and X<7

So combining 1 and 2 we get answer as X>9 and X<1 for this the question statement holds true.

So C is the answer.

+1Kudos if you like



Thanks
AB


I think your solution is clear enough.
I use different way but the result is the same
|x-4| = x - 4 when x>= 4 or |x-4| = 4 - x when x < 4, --> I have x>7 and x<1

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Re: Is |x - 6| > 2? [#permalink]

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New post 29 Sep 2014, 06:27
bhatiamanu05 wrote:
Is |x - 6| > 2?
Statement #1: |x - 4| > 3
Statement #2: |x - 8| > 1

the question statement : X-6>2 and X-6<-2 ==> X>8 and X<4

Statement #1 : X-4>3 and X-4<-3 ===> x>7 and X<1
Statement #2: X-8>1 and X-8<-1 ==> X>9 and X<7

So combining 1 and 2 we get answer as X>9 and X<1 for this the question statement holds true.

So C is the answer.

+1Kudos if you like

Thanks
AB


SO IF X =3 it follows x<4 but is not supported by our solution x<1.
??

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Is |x – 6| > 2? [#permalink]

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New post 17 Jul 2017, 10:07
Is |x – 6| > 2?

(1) |x – 4| > 3

(2) |x – 8| > 1

Last edited by Bunuel on 17 Jul 2017, 10:11, edited 1 time in total.
Renamed the topic and edited the question.

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Re: Is |x - 6| > 2? [#permalink]

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New post 17 Jul 2017, 10:14
Expert's post
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Re: Is |x - 6| > 2? [#permalink]

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New post 01 Sep 2017, 18:53
mikemcgarry wrote:
Is |x - 6| > 2?
Statement #1: |x - 4| > 3
Statement #2: |x - 8| > 1


For a discussion of inequalities and DS questions, as well as an efficient solution for this particular problem, see:
http://magoosh.com/gmat/2013/gmat-quant ... qualities/


Original Stmnt

x-6> 2
X > 8

-lx-6l>2
-x +6 >2
-x > -4
x< 4 - remember to flip

X>8 or x<4

Stmnt 1

x - 4 > 3
x >7

-|x - 4| > 3
-x +4 >3
-x > -1
x <1

Insuff
Stmnt 2

x - 8 > 1
x> 9

-|x - 8| > 1
-x +8 > 1
-x >-7
x< 7

Insuff

Stmnt 1 & 2

x>9 and x>1 - either satisfies the condition

C

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Re: Is |x - 6| > 2?   [#permalink] 01 Sep 2017, 18:53
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