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Is |x-1| < 1? (1) (x-1)^2 <= 1 (2) x^2 - 1 > 0

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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Mar 30, 2017 2:46 am
ziyuenlau wrote:Is |x-1| < 1?
(1) (x-1)² ≤ 1
(2) x² - 1 > 0
|a-b| = the distance between a and b.

Question stem, rephrased:
Is the distance between x and 1 less than 1?
In other words:
Is x between 0 and 2?
Translated into math:
Is 0 < x < 2?

Both statements are satisfied by x=2 (in which case the answer to the question stem is NO) and by x=1.5 (in which case the answer to the question stem is YES).
Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Mo2men » Thu Mar 30, 2017 4:40 am
GMATGuruNY wrote:
ziyuenlau wrote:Is|x-1| < 1?

(1) (x-1)² ≤ 1
(2) x² - 1 > 0
|a-b| = the distance between a and b.

Question stem, rephrased:
Is the distance between x and 1 less than 1?
In other words:
Is x between 0 and 2?
Translated into math:
Is 0 < x < 2?
Dear Mitch,
I have two questions:

1- In case above can I square the prompt as long as it positive?

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

I can rephrase it to be

Is x(x-2)<0?

Is it valid rephrasing?

2- In fact 1, how do I solve it algebraically when I have sign "<="?

Thanks
Last edited by Mo2men on Thu Mar 30, 2017 4:46 am, edited 1 time in total.
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by GMATGuruNY » Thu Mar 30, 2017 4:45 am
Mo2men wrote:Dear Mitch,
When you rephrased the question, you missed that x might be negative such as -1.5. It could make |x-1| < 1 true.

what do I miss??
x=-1.5 is not a viable option for |x-1| < 1.
If we plug x=-1.5 into |x-1|<1, we get:
|-1.5-1| < 1
|-2.5| < 1
2.5 < 1.
Doesn't work.
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by Mo2men » Thu Mar 30, 2017 4:47 am
GMATGuruNY wrote:
Mo2men wrote:Dear Mitch,
When you rephrased the question, you missed that x might be negative such as -1.5. It could make |x-1| < 1 true.

what do I miss??
x=-1.5 is not a viable option for |x-1| < 1.
If we plug x=-1.5 into |x-1|<1, we get:
|-1.5-1| < 1
|-2.5| < 1
2.5 < 1.
Doesn't work.
Sorry for the question, I was editing it when you was replying. i discovered it after sending question.

Thanks for your help
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