Is n^2 n^3 ? (1) n^2

Question

Is n^2 > n^3 ?

(1) n^2 < 1

(2) n^3 < 1

please help. This came in a Kaplan test and can't see why its E for the life of me

rvgmat12 · Answer

n can be 0 or a fraction less than one.

This satisfies both statements but gives contradictory results for the main question

0 - n^2 and n^3 are equal to 0

Fraction - n^3 is less than n^2

Hence E

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IanStewart · Answer

If n is negative, n^2 is always larger than n^3 (because then n^2 is positive and n^3 is negative, so n^2 > 0 > n^3 in that case). If n is between 0 and 1, then n^2 is also greater than n^3, because if we raise a 'fraction' (between zero and one) to a higher power, we get a smaller number.

Statement 1 means that n is between -1 and 1, and Statement 2 means that n is less than 1. In each case, with one exception (n = 0), the answer to the question must be 'yes'. The only reason the answer is E and not D here is because n can equal zero.

This is clearly a prep company question. The GMAT doesn't test weird exceptions around the number zero in the way this question does. If this were a real GMAT question, it would tell you n is nonzero in the question stem, and then the answer would be D, and it would be a better question.

I'd add that people who prefer algebra can use it here: we can rephrase the question "Is n^2 > n^3?" to find out under what conditions the answer is "yes". Dividing by n^2 on both sides, we get the simpler question "Is 1 > n?". We can (almost) safely divide by n^2 without needing to be concerned about whether to reverse the inequality, because n^2 is never negative. The only issue is that we might be dividing by zero, if n = 0, and we need to separate that out as a special case.

gmatbyexample · Answer

I recommend thinking about this from the range perspective AFTER ELIMINATING 0 as a possibility . In comparisons of powers, there are usually 4 ranges to think of. 1) n<-1 2) -11 When is n^2 > n^3? For every range except n>1 & except when n=0 (take some examples or see the link below) !! So the question now changes to: "Is n always <1 & n not equal to zero" because when n>1, the inequality doesn't hold. a) n^2 < 1 Trap alert! (dont forget the zero) - It could mean n is between -1 & 1. but n could be 0 too. So while it looks like SUFF, 0 spoils it. b) n^3 < 1 Similar trap here too. Combined, we cannot sufficiently discard 0 as a possibility. Combined, the ambiguity about n=0 remains, Hence (E). Here is an article for dealing with comparisons that may help: Inequalities Comparison Framework

Is n^2 > n^3 ? (1) n^2 < 1 (2) n^3 < 1

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