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Is |x-1|<1 for all integers x ?

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Is |x-1|<1 for all integers x ?

by VJesus12 » Tue Oct 24, 2017 3:24 pm
Is |x-1|<1 for all integers x ?

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

The OA is D.

I got confused here. I don't know how to prove statement (1) is sufficient.
By the other hand, if x<0 (statement 2), then |x-1|>1. Why is it sufficient?

Experts, if you could give me some help I'd be thankful.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Oct 24, 2017 9:44 pm
VJesus12 wrote:Is |x-1|<1 for all integers x ?

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

The OA is D.

I got confused here. I don't know how to prove statement (1) is sufficient.
By the other hand, if x<0 (statement 2), then |x-1|>1. Why is it sufficient?

Experts, if you could give me some help I'd be thankful.
Let's look at the inequality |x-1|<1 closely.

=> -1 < x - 1 < 1 => 0 < x < 2.

Question rephrased: Is 0 < x < 2?

(1) (x-1)^2 >1

=> |x-1| > 1. The result is opposite of what the question asks. The answer is NO. Sufficient.

(2) x < 0

Since the rephrased question asks whether 0 < x and the statement states that x < 0. The answer is NO. Sufficient.

The correct answer: D

Hope this helps!

-Jay

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