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Good Inequality Question

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Source: — Data Sufficiency |
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by imskpwr » Tue Jul 17, 2012 4:29 am
niketdoshi123 wrote:What is x?

1) |x| <2
2)|x| = 3x-2

From 1
x < 2
x > -2
Insufficient alone

From 2
x = 3x - 2
=> x=1

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

Insufficient alone
considering both, will give a unique solution.
I feel i should draw a number line as these q are mostly tricky.
Last edited by imskpwr on Tue Jul 17, 2012 4:38 am, edited 1 time in total.
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by Anurag@Gurome » Tue Jul 17, 2012 4:34 am
niketdoshi123 wrote:What is x?

1) |x| <2
2)|x| = 3x-2
Statement 1: -2< x < 2

Not sufficient

Statement 2: 3x = |x| + 2
As |x| is always greater than or equal to zero, (|x| + 2) must be positive.
Hence, x is positive.
Hence, |x| = x
Hence, x = (3x - 2) ---> x = 1

Sufficient

The correct answer is B.
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by Anurag@Gurome » Tue Jul 17, 2012 4:38 am
imskpwr wrote:From 2
x = 3x - 2 (Here you are assuming |x| = x, i.e. x is positive)
=> x=1 (You've got x = 1 which is positive. So the solution is okay)

x = -3x + 2 (Here you are assuming |x| = -x, i.e. x is negative)
=> x = 1/2 (But you've got x = 1/2 which is positive. So the solution is not valid as it contradicts your initial assumption)
Hope that helps.
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by niketdoshi123 » Tue Jul 17, 2012 6:18 am
The OA is B.
Anurag@Gurome wrote:
niketdoshi123 wrote:What is x?

1) |x| <2
2)|x| = 3x-2
Statement 1: -2< x < 2

Not sufficient

Statement 2: 3x = |x| + 2
As |x| is always greater than or equal to zero, (|x| + 2) must be positive.
Hence, x is positive.
Hence, |x| = x
Hence, x = (3x - 2) ---> x = 1

Sufficient

The correct answer is B.
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by imskpwr » Tue Jul 17, 2012 7:18 am
Anurag@Gurome wrote:
imskpwr wrote:From 2
x = 3x - 2 (Here you are assuming |x| = x, i.e. x is positive)
=> x=1 (You've got x = 1 which is positive. So the solution is okay)

x = -3x + 2 (Here you are assuming |x| = -x, i.e. x is negative)
=> x = 1/2 (But you've got x = 1/2 which is positive. So the solution is not valid as it contradicts your initial assumption)
Hope that helps.
Thanks Anurag Sir. I believe that was a fatal error.
I think quant section has more FREQUENT visits from instructors. Not a single q is left unanswered.
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