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Is n-1>0?

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by paresh_patil » Mon Mar 04, 2013 4:56 am
If n is an integer, is n-1>0?

1) n^2-n>0
2) n^2=9

Answer-E

I know that statement 2 is insufficient.
I need explanation on why statement 1 is not sufficient.
If you divide the inequality by n, can statement 1 stand sufficient?
Please help.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Mon Mar 04, 2013 5:04 am
paresh_patil wrote:If n is an integer, is n-1>0?

1) n^2-n>0
2) n^2=9
Statement 1: n² - n > 0 ---> n(n - 1) > 0
This means either n and (n - 1) are of same sign.
Hence, it is possible that,
  • Both are positive ---> (n - 1) > 0
    Both are negative ---> (n - 1) < 0
Not sufficient

Statement 2: n² = 9 --> n = ±3

Not sufficient

1 & 2 Together: As n = ±3, either (3 - 1) > or (-3 - 1) < 0

Not sufficient

The correct answer is E.
paresh_patil wrote:If you divide the inequality by n, can statement 1 stand sufficient?
Never multiply or divide an inequality with a variable unless you know for sure that the variable can have only positive or only negative values. This is because dividing or multiplying an inequality with negative numbers change the inequality sign but doing so with positive numbers retains the same sign.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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