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CEO
Joined: 21 Jan 2007
Posts: 2797
Location: New York City
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[0], given: 4
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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
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CEO
Joined: 17 Nov 2007
Posts: 3608
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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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
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SVP
Joined: 28 Dec 2005
Posts: 1612
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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.
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Director
Joined: 12 Jul 2007
Posts: 875
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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.
Answer E
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