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If n is positive and less than 1, then which of the following is true?

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If n is positive and less than 1, then which of the following is true? [#permalink]

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New post 15 Mar 2017, 07:11
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Question Stats:

83% (00:45) correct 17% (01:15) wrong based on 47 sessions

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If n is positive and less than 1, then which of the following is true?

(I) n^2 - n < 0
(II) n^3 < n
(III) n + 1 < 1

A) (I) only
B) (II) only
C) (III) only
D) (I) and (II) only
E) (II) and (III) only
[Reveal] Spoiler: OA

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If n is positive and less than 1, then which of the following is true? [#permalink]

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New post 15 Mar 2017, 07:50
Plug in numbers: my example = \(\frac{1}{2}\)


(1) \(\frac{1}{2}\)^2 - \(\frac{1}{2}\) < 0

=> \(\frac{1}{4}\) - \(\frac{1}{2}\) < 0 correct

(2) \(\frac{1}{2}\)^3 < \(\frac{1}{2}\)

\(\frac{1}{8}\) < \(\frac{1}{2}\) correct

(3) \(\frac{1}{2}\) + 1 < 1 wrong!
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Re: If n is positive and less than 1, then which of the following is true? [#permalink]

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New post 28 Nov 2017, 12:27
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Hi All,

When dealing with Roman Numeral questions, you can work through the 3 Roman Numerals in any order (and eliminate answers according to your results). For this question though, I'll work through all 3 options in order:

We're told that N is POSITIVE and LESS than 1. This means that 0 < N < 1. We're asked which of the Roman Numerals is true (meaning which is ALWAYS true no matter how many different examples we can come up with). This question can be solved with a mix of logic and TESTing VALUES.

I. N^2 - N < 0

Since N is a POSITIVE FRACTION - and squaring a positive fraction will always lead to a SMALLER fraction - we know that N^2 will always be less than N.
For example, (1/2)^2 = 1/4.
Thus N^2 - N will ALWAYS be less than 0.
Roman Numeral 1 IS always true.

II. N^3 < N

The same logic we used in Roman Numeral 1 applies to Roman Numeral 2. Cubing a positive fraction will ALWAYS lead to a SMALLER fraction, so N^3 will always be less than N.
For example, (1/2)^3 = 1/8
Roman Numeral 2 IS always true.

III. N+1 < 1

We're told that N is POSITIVE, so N+1 will be greater than 1.
Roman Numeral 3 is NOT true.

Final Answer:
[Reveal] Spoiler:
D


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Kudos [?]: 3700 [1], given: 173

Re: If n is positive and less than 1, then which of the following is true?   [#permalink] 28 Nov 2017, 12:27
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If n is positive and less than 1, then which of the following is true?

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