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# What is x? (1) |x| < 2 (2) |x| = 3x 2

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Manager
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What is x? (1) |x| < 2 (2) |x| = 3x 2 [#permalink]  23 Sep 2007, 22:06
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What is x?

(1) |x| < 2

(2) |x| = 3x – 2
GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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St1:
x could be 1,0,-1,-2...etc
Insufficient.

St2:
x must be greater than 2/3. Insufficient.

Using both st1 and st2:
x > 1, so 2/3 < |x| < 2. x could be any fraction or integer withthin this range. Insufficient.

Ans E
Director
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Re: DS : Absolutes [#permalink]  23 Sep 2007, 22:53
carpeD wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x – 2

1) x < 2, x > -2
so the final range is -2 < x < 2
cannot tell what x could be -1, 0, 1/2, NSF

2) for x > 0, x = 3x - 2 ---> 2x = 2 therefore x = 1
for x < 0, x = -(3x - 2) ---> x = -3x + 2 = 4x = 2 there x = 1/2
x could be 1/2 or 1, NSF

combining 1) and 2)
-2 < x < 2 & x = 1/2 or 1

we see that both x could still be 1/2 or 1

darn right logic but silly calculation error... will go for E now!

Last edited by beckee529 on 24 Sep 2007, 06:35, edited 2 times in total.
CEO
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Re: DS : Absolutes [#permalink]  24 Sep 2007, 00:13
carpeD wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x – 2

S1: X can be anything btwn -2<x<2> -2x=-2---> x=1

or

x=-3x+2 ---> 4x=2 ---> x=1/2

Two values insuff.

S1 and S2:

-2<x<2 and X=1 or 1/2

Insuff.

E.
Senior Manager
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Re: DS : Absolutes [#permalink]  24 Sep 2007, 02:45
carpeD wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x – 2

(1) -2<x<2 insufficient
(2) if x>0 => x=3x-2 (x=1) => OK
If x<0 x=-3x+2 (x=1/2) => not OK
So x=1
Manager
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I will go with B as well. What's the OA.

(1) |x| < 2 implies -2<x<2>0 => x=3x-2 (x=1) => OK
If x<0> not OK because x < 0

Hence x=1 only. Hence choice B is sufficient.
_________________

Regards

Subhen

Senior Manager
Joined: 27 Aug 2007
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I also got E,

1) x<2>-2 thus INSUFF
2) x=1 and x=0.5 which also INSUFF

together 1 and 0.5 can satisfy the equation.

Ans: E
Director
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Re: DS : Absolutes [#permalink]  24 Sep 2007, 09:25
Also go for B,

1st: insuff 2<x<-2
2nd: x>0, 3x-2=x, thus x=1. when x>0, x=1 and

if x<0, 2-3x=x, thus x=1/2. when x<0, x=1/2------> no solution.

thus 2nd statement gives only one possible solution..
Director
Joined: 11 Jun 2007
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very good catch.. i forgot to plug in to see if the solution works! also agreed with B since 1/2 cannot work.. whats the OA?
Director
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Re: DS : Absolutes [#permalink]  24 Sep 2007, 23:16
carpeD wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x – 2

from stat 1 x can be 0 or 1. Insuff.

from stat 2 x can only be 1 (x cannot be 1/2 when x<0)
Re: DS : Absolutes   [#permalink] 24 Sep 2007, 23:16
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