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# is |x-1| < 1? (x-1)^2 is less than or equal to 1 x^2 - 1

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CEO
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is |x-1| < 1? (x-1)^2 is less than or equal to 1 x^2 - 1 [#permalink]  27 Dec 2007, 11:46
is |x-1| < 1?

(x-1)^2 is less than or equal to 1
x^2 - 1 is greater than 0
CEO
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[#permalink]  27 Dec 2007, 12:21
E

|x-1| < 1 is true for x e (0,2)

1.(x-1)²<=1 ==> |x-1|<=1 ==> x e [0,2]. insuff.
2. x²-1>0 ==> x²>1 ==> x e (-∞,-1)&(1,+∞). insuff.
1&2 x e [0,2]&((-∞,-1)&(1,+∞)) ==> x e (1,2]. insuff

for example,
x=1.5 and x=2 - both satisfied conditions 1 and 2 but

|1.5-1|=0.5<1 true
|2-1|=1<1 false
SVP
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[#permalink]  27 Dec 2007, 12:28
I am getting E.

The expression can be simiplified to ask if 0<x<2

statement 1 says that x<=2 ... not sufficient

statement 2 says that x can be less than or equal to -1, or, greater than or equal to +1. not sufficient.

put them together, and you still cant come up with a definitive answer.
Director
Joined: 12 Jul 2007
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[#permalink]  27 Dec 2007, 12:31
is |x-1| < 1? rephrase question

2 > x > 0? or is x between 0 and 2 (non inclusive)

1. (x-1)^2 is less than or equal to 1

tells us that x is between 0 and 2 (inclusive). almost sufficient, but this says X can be 0 or 2 (or anywhere in between), the question is asking if it's between 0 and 2. INSUFFICIENT

2. x^2 - 1 is greater than 0

tells us that x^2 is greater than 1 so x is greater than 1 or less than -1. INSUFFICIENT

taken together we know that X is between 0 and 2 inclusive and less than -1 or greater than 1 not inclusive. combining these we see that...

1 < x <= 2 which is NOT sufficient to solve 2 > x > 0 only because they don't rule out the number 2.

[#permalink] 27 Dec 2007, 12:31
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