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

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Senior Manager
Joined: 02 Jan 2017
Posts: 312
If n is positive and less than 1, then which of the following is true?  [#permalink]

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15 Mar 2017, 08:11
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Difficulty:

15% (low)

Question Stats:

78% (01:02) correct 22% (01:16) wrong based on 64 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
Intern
Joined: 09 Jan 2017
Posts: 22
Location: Germany
GPA: 3.7
If n is positive and less than 1, then which of the following is true?  [#permalink]

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15 Mar 2017, 08:50
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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28 Nov 2017, 13:27
1
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.

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Re: If n is positive and less than 1, then which of the following is true? &nbs [#permalink] 28 Nov 2017, 13:27
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