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simple but tricky

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Source: — Data Sufficiency |

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by Anurag@Gurome » Sat Jul 16, 2011 3:18 am
gmat25 wrote:What is x?

(1) |x| < 2
(2) |x| = 3x - 2
Statement 1: |x| < 2 ---> -2 < x < 2 ---> NOT sufficient

Statement 2: |x| = 3x - 2
If x ≥ 0, x = 3x - 2 ---> x = 1
If x < 0, -x = 3x - 2 ---> x = 1/2 ---> Not possible

Hence, x = 1

Sufficient

The correct answer is B.
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by beatthegmat.garry » Sat Jul 16, 2011 5:32 pm
Thank you for your reply, but why do you say that x=1/2 value is not possible? It doesnt mention in the question that x is an integer.

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by Frankenstein » Sat Jul 16, 2011 8:54 pm
beatthegmat.garry wrote:Thank you for your reply, but why do you say that x=1/2 value is not possible? It doesnt mention in the question that x is an integer.

Regards!
Hi,
If x < 0, -x = 3x - 2 ---> x = 1/2 ---> Not possible
We get x = 1/2, when we have considered the case x<0. So, it is impossible.
Moreover, whenever in doubt just plug in that value in the equation
Check if |1/2| = 3(1/2) -2
LHS is 1/2,
RHS = -1/2.
Cheers!

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