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# Is n>0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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14 Jul 2017, 01:01
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Difficulty:

35% (medium)

Question Stats:

72% (01:31) correct 28% (01:45) wrong based on 50 sessions

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Is n>0?

1) n>-1
2) |1+n| > |n-3|

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Re: Is n>0?  [#permalink]

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14 Jul 2017, 01:16
MathRevolution wrote:
Is n>0?

1) n>-1
2) |1+n| > |n-3|

(1) Insufficient.

(2) \(|1+n| > |n-3| \implies |1+n|^2 > |n-3|^2 \implies n^2+2n+1 > n^2-6n+9 \implies 8n > 8 \implies n > 1 >0 \). Sufficient.

The answer is B.
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Re: Is n>0?  [#permalink]

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14 Jul 2017, 01:20
MathRevolution wrote:
Is n>0?

1) n>-1
2) |1+n| > |n-3|

1) n>-1
Insufficient. n = -0.4 or n = 3

2) |n+1| > |n-3|
If n < 0, then the left hand size will always be smaller than the right hand side => n>0

n = 0.5
|n+1| = 1.5
|n-3| = 2.5 (Not allowed by the statement)

n = 1
|n+1| = 2
|n-3| = 2 (Not allowed by the statement)

n = 1.1
|n+1| = 2.1
|n-3| = 1.9

n>1

Sufficient. B is the answer.
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Re: Is n>0?  [#permalink]

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16 Jul 2017, 18:44
==> In the original condition, there is 1 variable (n), and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. Also, for inequality questions, if the range of the question includes the range of the condition, the condition is sufficient. Thus, for con 1), the range of the question does not include range of the condition, hence it is not sufficient. For con 2), if you square both sides, you get |1+n|^2 > |n-3|^2, (1+n)^2 > (n-3)^2, n^2+2n+1>n^2-6n+9, 8n>8, n>1, so the range of the question includes the range of the condition, hence it is sufficient.

Therefore, the answer is B.
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Re: Is n>0?   [#permalink] 16 Jul 2017, 18:44
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# Is n>0?

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