Is |x - 6| 2? (1) |x - 4| 3 (2) |x - 8| 1

Question

Is |x - 6| > 2?

(1) |x - 4| > 3
(2) |x - 8| > 1

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

Show Answer

Official Answer

C

bhatiamanu05 · Accepted Answer

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

Spunkerspawn · Answer

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

Puneethrao · Answer

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

vad3tha · Answer

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 Already +1 Kudos for you

earnit · Answer

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

Nunuboy1994 · Answer

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

ShashwatPrakash · Answer

Is |x - 6| > 2? Statement #1 : |x - 4| > 3 Statement #2 : |x - 8| > 1 So the question basically asks us is if: x > 8 OR x < 4 Statement #1: |x - 4| > 3 tells us that x > 7 or x < 1--So this statement does satisfy the second condition (x<4) Statement #2: |x - 8| > 1 tells us that x > 9 or x < 7--So this statement does satisfy the first condition (x>8) Bunuel Please explain me what I am doing wrong.

pushpitkc · Answer

Hey  ShashwatPrakash

The highlighted portion is your only mistake. 
Now, because the range of the inequality is x>8 and x<4, the only possibility is when we
combine the information from both the sentences. Hence, the answer is  Option C

Hope this helps you

srinjoy1990 · Answer

CEdward · Answer

mikemcgarry  Hi Mike, I did all of the dirty work above and got the exact same solution, but I don't understand how I got there. Can you explain why the statements individually are insufficient? Secondly, can you explain why the final answer is x > 9 and x < 1? Why those particular ranges?

bumpbot · Answer

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Is |x - 6| > 2? (1) |x - 4| > 3 (2) |x - 8| > 1

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