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If n ≠ 0, which of the following must be greater than n?

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If n ≠ 0, which of the following must be greater than n? [#permalink]

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New post 22 May 2016, 13:53
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53% (00:37) correct 47% (00:37) wrong based on 142 sessions

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If n ≠ 0, which of the following must be greater than n?

I. 2n
II. n^2
III. 2 - n

A. I only
B. II only
C. I and II only
D. II and III only
E. None
[Reveal] Spoiler: OA

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Kudos [?]: 132827 [2], given: 12378

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Re: If n ≠ 0, which of the following must be greater than n? [#permalink]

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New post 22 May 2016, 21:47
Bunuel wrote:
If n ≠ 0, which of the following must be greater than n?

I. 2n
II. n^2
III. 2 - n

A. I only
B. II only
C. I and II only
D. II and III only
E. None


n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)

but if n = positive:

n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only II
=>answer is B

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Re: If n ≠ 0, which of the following must be greater than n? [#permalink]

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New post 23 May 2016, 11:43
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Bunuel wrote:
If n ≠ 0, which of the following must be greater than n?

I. 2n
II. n^2
III. 2 - n

A. I only
B. II only
C. I and II only
D. II and III only
E. None


Plug in some value for n

Let n = 1

I. 2n = 2 ( Greater than n)

II. n^2 = 1 ( equal to n)

III. 2 - n = 1 ( equal to n)

Check with a negative number

Let n = - 1

I. 2n = -2 ( not greater than n)

II. n^2 = 1 ( Greater than n )

III. 2 - n = 3 ( not greater than n)


Thus we can not confirm, answer will be (E)
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Re: If n ≠ 0, which of the following must be greater than n? [#permalink]

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New post 29 Sep 2017, 08:48
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If n ≠ 0, which of the following must be greater than n?

I. 2n
II. n^2
III. 2 - n

A. I only
B. II only
C. I and II only
D. II and III only
E. None

If n ≠ 0, then n can be positive, negative or fraction. If we can prove that the result is a smaller number then we can eliminate the answer choice.
I. 2n
Try negative -2, result is -4 which is less then 2n. Eliminate a and c.

II. n^2
If n=1/2 the result will be 1/4 which is less then n. Eliminate b and d.

III. 2 - n

E is the only choice left and is our answer.

Kudos [?]: 15 [0], given: 76

Re: If n ≠ 0, which of the following must be greater than n?   [#permalink] 29 Sep 2017, 08:48
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If n ≠ 0, which of the following must be greater than n?

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