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/
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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

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
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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

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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