If −1

Question

If −1 < n < 0 , which of the following inequalities must be true? I. n^4 > n^3 II. n^5 > n^3 III. n^4 − n^5 > n^2 − n^3 (A) None (B) I only (C) III only (D) I and II only (E) I and III only

TestPrepUnlimited · Answer

I. We may divide both sides by  n^2  first since that must be positive. n^2 > n  is  true  since Positive > Negative.

II.  n^3 > n . We may plug in an  n  to check if it is true.  n = -0.5  gives  -0.125 > -0.5 .  True.

Note at this point we already choose D as we can eliminate every other option.

III. Divide both sides by  n^2  first.  n^2 - n^3 > 1 - n .

Then factor n^2 on the left side to get  n^2(1 - n) > 1 - n .

We know  1 - n  is positive, divide both sides by that to get  n^2 > 1  which is  false.

Ans: D

UUBA · Answer

For option 3, if we take n^4 and n^2 out, (1-n) will be a positive number on both sides. Hence n^4 should be less than n^2 because the value of n lies between 0 and -1 or the magnitude lies between 0 and 1. The bigger the power, the smaller the value.

If −1 < n < 0, which of the following inequalities must be true

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