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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0

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Joined: 19 Jul 2008
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Is |x|< 1? (1) |x + 1| = 2|x - 1| (2) |x - 3| 0 [#permalink]

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25 Aug 2008, 09:34
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Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0

Kudos [?]: 12 [0], given: 0

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Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1062 [0], given: 5

Location: New York

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25 Aug 2008, 09:52
gmatcraze wrote:
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0

(1) |x + 1| = 2|x - 1|

x+1>0 and x-1>0 --> x>0
x+1= 2(x-1) --> x=3 --------(1)
x+1>0 and x-1<0 --> x>-1 and x<1
x+1=- 2(x-1) --> x=1/3 --------(2)
x+1<0 and x-1<0 --> x<-1 and x<1 --> x<-1
-( x+1)= -2(x-1) --> x=3 ( Not possible)
x+1<0 and x-1>0 --> x<-1 and x>1
x=1/3 ( Not possible)

from (1) and (2) two solutions insuffcieint.
|x|>1 and |x|<1

2) |x - 3| ≠ 0
x-3>0 or x-3<0
-- |x|>3 --> |x|>1
x-3<0 |x|<1 (possible when e.g x=2.5)
two solutions
insuffcient

Commbine both

Still two solutions possible
E

What is OA
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Joined: 06 Apr 2008
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25 Aug 2008, 10:16
gmatcraze wrote:
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0

Statement 1) is true for x=3 and x=1/3 so insuff.

Statement 2) is true for x != 3

Combining both x=1/3

IMO C)

Kudos [?]: 165 [0], given: 1

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Joined: 07 Nov 2007
Posts: 1792

Kudos [?]: 1062 [0], given: 5

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25 Aug 2008, 10:31
nmohindru wrote:
gmatcraze wrote:
Is |x|< 1?
(1) |x + 1| = 2|x - 1|
(2) |x - 3| ≠ 0

Statement 1) is true for x=3 and x=1/3 so insuff.

Statement 2) is true for x != 3

Combining both x=1/3

IMO C)

Your are right ! I overlooked that.

Agree with C.
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Re: absolute value problem   [#permalink] 25 Aug 2008, 10:31
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