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Inequality and absolute value

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Inequality and absolute value

by Brent@GMATPrepNow » Mon Feb 06, 2012 2:19 pm
I made up this question while in the shower and thought I'd post it.

Is |x| > 0?

1) 5(x^2)(y^3) < 0

2) (3y^3 - 3xy + 3x^3)/3x > 0

Hint: This one is an excellent candidate for rephrasing the target question.

Cheers,
Brent
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Feb 06, 2012 2:47 pm
Brent@GMATPrepNow wrote:I made up this question while in the shower and thought I'd post it.

Is |x| > 0?

1) 5(x^2)(y^3) < 0

2) (3y^3 - 3xy + 3x^3)/3x > 0

Hint: This one is an excellent candidate for rephrasing the target question.

Cheers,
Brent
Target question: Is |x| > 0

Notice that the absolute value of ANY number will be greater than or equal to 0. In fact, there's only one way that |x| is not greater than 0. If x=0, then |x| is not greater than 0.

So, we could rephrase the target question as: Does x equal any number other than zero?
An even better way to rephrase the target question is to ask, Does x=0?
If we know the answer to this question, then we know the answer to the question "Is |x| > 0?"

Now that we've rephrased the target question as "Does x=0?" we're ready to check the statements.

Statement 1: 5(x^2)(y^3) < 0
If 5(x^2)(y^3) < 0, then we can be certain that x does not equal 0. (If x=0, then 5(x^2)(y^3) = 0)
As such, statement 1 is SUFFICIENT


Statement 2: (3y^3 - 3xy + 3x^3)/3x > 0
If x=0, then (3y^3 - 3xy + 3x^3)/3x is undefined. Therefore, if x=0, then (3y^3 - 3xy + 3x^3)/3x could not be greater than zero.
Since (3y^3 - 3xy + 3x^3)/3x > 0, we can be certain that x does not equal 0.
As such, statement 2 is SUFFICIENT

The answer is D

Cheers,
Brent
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by neelgandham » Mon Feb 06, 2012 2:59 pm
|x| is always > 0. So the question can be rephrased to

Does x!=0?
1) 5(x^2)(y^3) < 0
- The value x is definitely not 0 because the value of 5(x^2)(y^3) would be 0, if x is 0. So statement 1 is sufficient to answer the question
2) (3y^3 - 3xy + 3x^3)/3x > 0
- The value x is definitely not 0 because the value of (3y^3 - 3xy + 3x^3)/3x would be undefined if it is 0. So statement 2 is sufficient to answer the question

IMO D
Anil Gandham
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