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If n is positive and less than 1...

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by BTGmoderatorLU » Sat Oct 28, 2017 8:24 am
If n is positive and less than 1, then which of the following is true?

$$(1)\ n^2-n<0$$
$$(2)\ n^3<n$$
$$(3)\ n+1<1$$

A) (1) only
B) (2) only
C) (3) only
D) (1) and (2) only
E) (2) and (3) only

The OA is D.

I don't understand why D is the correct answer. Can any expert help me with this PS question, please? Thanks.
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by [email protected] » Sat Oct 28, 2017 10:52 am
Hi LUANDATO,

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: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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