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If X \ge 1 , then the inequality turns into X - 1 \lt 1 or X \lt 2 . If X \lt 1 , then the inequality turns into 1 - X \lt 1 or X \gt 0 . Combine the intervals to get the answer.

If X \ge 1 , then the inequality turns into X - 1 \lt 1 or X \lt 2 . If X \lt 1 , then the inequality turns into 1 - X \lt 1 or X \gt 0 . Combine the intervals to get the answer.

|1-x|<{1} --> key point is x=1 (key points are the values of x when absolute values equal to zero), thus two ranges to check:

x<1 --> |1-x|=1-x and |1-x|<{1} becomes: 1-x<{1} --> x>0; x\geq{1} --> |1-x|=-1+x and |1-x|<{1} becomes: -1+x<{1} --> x<2;

So |1-x|<{1} holds true for 0<x<2.

Answer: D.

As for your question: x can not equal to 2, because 0<x<2 means that x MUST be less than 2 (and more than zero), for ANY x from this range given inequality will hold true.

I guess (0,2) should be changed to 0<x<2 (as well as all other options) to avoid confusion whether 0 and 2 are inclusive in the range.

If X \ge 1 , then the inequality turns into X - 1 \lt 1 or X \lt 2 . If X \lt 1 , then the inequality turns into 1 - X \lt 1 or X \gt 0 . Combine the intervals to get the answer.

|1-x|<{1} --> key point is x=1 (key points are the values of x when absolute values equal to zero), thus two ranges to check:

x<1 --> |1-x|=1-x and |1-x|<{1} becomes: 1-x<{1} --> x>0; x\geq{1} --> |1-x|=-1+x and |1-x|<{1} becomes: -1+x<{1} --> x<2;

So |1-x|<{1} holds true for 0<x<2.

Answer: D.

As for your question: x can not equal to 2, because 0<x<2 means that x MUST be less than 2 (and more than zero), for ANY x from this range given inequality will hold true.

Hope it helps.

Thanks for the quick reply! Your explanation with the key-point value is very helpful!

Also, I was not aware, that if they talk about "range" the values given are excluded (hence 0<x<2 )

Re: GMAT Club - m11#16 [#permalink]
14 Jun 2011, 23:35

quoting bunuel :

" I guess (0,2) should be changed to 0<x<2 (as well as all other options) to avoid confusion whether 0 and 2 are inclusive in the range. "

This correction is needed IMO. when we say (0,2) we mean than the numbers are included. Also another alternative would be to change the question to |1-x|<=1 _________________

Cheers !!

Quant 47-Striving for 50 Verbal 34-Striving for 40