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# Is |x-1| < 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
Re: Is |x-1| < 1?  [#permalink]

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14 Jun 2017, 22:38
csaluja wrote:
Hi,

I got the right answers as my final equations however, I chose D instead of E. For S1, I got x= 0 or 2. If you plug these two in the original equation, you can "no" as an answer which I thought was sufficient. For S2, I got x= -1 or 1. Again, I plugged both of these numbers in and got "no" as an answer as well. Could anyone please explain how both of these equations are insufficient even when we are getting "no" as an answer? Please help!

The values you got are not correct. We get ranges from each statement, not exact values. Notice that we are NOT told that x is an integer.

The question asks is 0 < x < 2?

(1) gives 0 <= x <= 2. If x = 0, the answer is NO but if x = 1, then the answer is YES. Not sufficient.

(2) gives x<-1 or x>1. If x = -10, the answer is NO but if x = 1.5, then the answer is YES.Not sufficient.

(1)+(2) gives 1 < x <= 2. If x = 2, the answer is NO but if x = 1.5, then the answer is YES. Not sufficient.

Hope it's clear.
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Joined: 09 Mar 2018
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Re: Is |x-1| < 1?  [#permalink]

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06 Jun 2018, 19:39
I have a question for experts plz help me if for the same question we faced a statement (x-1)^2<1 or (x-1)^2>1 what the options we selected ? Plz help
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Re: Is |x-1| < 1?  [#permalink]

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07 Jun 2018, 00:08
Krishaa12 wrote:
I have a question for experts plz help me if for the same question we faced a statement (x-1)^2<1 or (x-1)^2>1 what the options we selected ? Plz help

Hello

For this question, if we change the first statement to
(1) (x-1)^2 < 1

Then we will get 0 < x < 2, same thing that the question asks. In that case, first statement will be sufficient to answer the question with a YES.

Also if we change the first statement to
(1) (x-1)^2 > 1

Then we will get that either x < 0 or x > 2. In that case, first statement will be sufficient to answer the question with a NO.
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Joined: 15 Jan 2017
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Re: Is |x-1| < 1?  [#permalink]

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23 Jul 2018, 00:39
Picked E:

St 1: (x-1)^2<= 1
we get x(x-2)<= o
so x<= 2and x>= 0
Plugging in --> |2-1| not greater than 1. But next value, x =1 (if we think of x as less than 2), its |1-1|> so true.

St 2: x^2 > 1
Means --> -1 < x < 1. so if X was 0 the condition would not hold. But if X was -0.5, it would hold. So two answers.

St 1 and St 2 --> x is both negative and positive --> x<=2 and x > 0 and -1<x<1. Some values fit while others don't. Answer E.
Re: Is |x-1| < 1?   [#permalink] 23 Jul 2018, 00:39

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