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

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Manager
Joined: 04 Jan 2008
Posts: 117
What is x? (1) |x| < 2 (2) |x| = 3x 2 [#permalink]

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23 Sep 2008, 05:04
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What is x?

(1) |x| < 2

(2) |x| = 3x – 2
Director
Joined: 01 Jan 2008
Posts: 605

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23 Sep 2008, 06:48
dancinggeometry wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x – 2

1: insufficient because any x between - 2 and 2 qualify
2: sufficient: obviously x > 0 because 3x-2 = |x| >= 0 -> x >= 2/3.
draw y = x and y = 3x - 2 -> one solution

SVP
Joined: 29 Aug 2007
Posts: 2457

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23 Sep 2008, 14:41
maratikus wrote:
dancinggeometry wrote:
What is x?

(1) |x| < 2

(2) |x| = 3x – 2

1: insufficient because any x between - 2 and 2 qualify
2: sufficient: obviously x > 0 because 3x-2 = |x| >= 0 -> x >= 2/3.
draw y = x and y = 3x - 2 -> one solution

B.
1: if |x| < 2, x has wide range of possibilities.
2: if |x| = 3x – 2, "x = 3x – 2" yields x = 1 and "x = - 3x + 2" yeilds x = 1/2.
x = 1/2 doesnot satisfy the equation where as x = 1 does.
so x = 1.

//B//
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Re: Zumit PS 026   [#permalink] 23 Sep 2008, 14:41
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# What is x? (1) |x| < 2 (2) |x| = 3x 2

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