Is |x-1| < 1 ? 1. (x-1)^2 >1 2. x < 0 GMAT Data Sufficiency

Question: Is |x-1| < 1 ?

1. (x-1)^2 >1
2. x < 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

‘Is |x-1| < 1 ?’ – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. 
GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions. Data sufficiency assesses candidates’ critical thinking and hypervigilance. An abstract problem-solving question is mainly given and most of the difficulty comes from obtuse or clever wording, candidates usually miss it.

Solution and Explanation 

Approach Solution 1

let us solve the Question stem and see what information is it asking—
|x-1|<1
This suggests that x should be between 0 and 2 and that its distance from 1 should be less than 1.
Now we can solve both options
Statement 1
x-1<1
x<2

Statement 2
(x-1)<1
x-1>-1
x>0

This means the question ask - IS 0<x<2?

Now lets evaluate the statements
Statement 1
(x-1)^2 >1

this gives us two solutions

1.  if x<0, the answer is always yes
2.  if x>0, then x>2..

so will tell us either x<0 or x>2
so answer is NO
Statement 1 is Sufficient

Statement 2
x < 0
Here it is told x <0..
so x can not lie between 0 and 2
So answer Is NO
Statement 2 is Sufficient
The answer is D which is EACH statement ALONE is sufficient.

Correct Answer: D

Approach Solution 2

There is another approach to solve the question. Let us use DS approach and test extremes
Let x = 1000

Looking at statement 1
(x-1)^2 >1
since (1000-1)^2 is much greater than 1.
therefore, answer the question. Is |1000-1| < 1?
No. It's greater.
Next, consider what you would need to accomplish to receive a different response, in this case, a yes.
A significantly smaller value of x would be required.
The least positive value of x that might be able to satisfy the assertion is around 2.0001.
However, that likewise yields a "no" response because |2.0001-1| is still higher than 1.
Additionally, try a negative value. x = -0.5 is valid. But once more, |-0.5-1| exceeds 1, hence the answer is "no."
The statement is sufficient if you always receive a "no."

Looking at statement 2
x < 0

Its same situation as statement 1, if we test a couple of negative values of x we will notice that we will always get a 'no',
so statement 2 is sufficient.
The answer is D which is EACH statement ALONE is sufficient.

Correct Answer: D

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