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

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!!

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

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

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

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.

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
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x<4 | x >8 => Yes.

1. x < 1 | x > 7 => Yes | May be => insufficient.
2. x < 7 | x > 9 => May be | Yes.
1+2 => common regions x < 1 | x > 9 => Yes | Yes.

I used the number line approach.
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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?
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