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# If n > 0 , which of the following must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
If n > 0 , which of the following must be true?  [#permalink]

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12 May 2016, 01:55
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Difficulty:

35% (medium)

Question Stats:

66% (01:02) correct 34% (01:01) wrong based on 218 sessions

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If n > 0 , which of the following must be true?

I n^2 > 1
II n - n^2 < 0
III 2n - 1 > 0

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

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Posts: 104
Re: If n > 0 , which of the following must be true?  [#permalink]

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12 May 2016, 03:43
IMO E

take n as 0.1 or 0.001, all the statements wont be true
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Re: If n > 0 , which of the following must be true?  [#permalink]

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12 May 2016, 08:12
Bunuel wrote:
If n > 0 , which of the following must be true?

I n^2 > 1
II n - n^2 < 0
III 2n - 1 > 0

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

I. True for all values of n except 1

When n = 1 ; n^2 = 1

II. True for all values of n except 1

When n = 1 ; n - n^2 = 1 - 1 =>0

III True for all values of n

Hence the correct answer will be (E)
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Re: If n > 0 , which of the following must be true?  [#permalink]

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12 May 2016, 09:37
Abhishek009 wrote:
Bunuel wrote:
If n > 0 , which of the following must be true?

I n^2 > 1
II n - n^2 < 0
III 2n - 1 > 0

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

I. True for all values of n except 1

When n = 1 ; n^2 = 1

II. True for all values of n except 1

When n = 1 ; n - n^2 = 1 - 1 =>0

III True for all values of n

Hence the correct answer will be (E)

I not true for anything <1. ~0.5
II not true for anything <1
III not true for anything <0.5
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Re: If n > 0 , which of the following must be true?  [#permalink]

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13 Oct 2018, 03:31
Bunuel wrote:
If n > 0 , which of the following must be true?

I n^2 > 1
II n - n^2 < 0
III 2n - 1 > 0

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

Note: n is positive but we don't know whether it is an integer or fraction.

I. n^2>1. NOT necessarily . let x be 1/2.

II. n - n^2 <0. Let x be 1/2. False.

III. 2n - 1 > 0. let x be 1/2. 2*1/2 - 1 =0. False.

Thus , none of these options are correct. This question is designed to test fractional case.

Re: If n > 0 , which of the following must be true?   [#permalink] 13 Oct 2018, 03:31
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