Is 5^n 25 (2) n^3

Question

Is  5^n < 0.04 ?

(1)  (\frac{1}{5})^n > 25

(2)  n^3 < n^2

Bunuel · Accepted Answer

Is 5^n < 0.04 ? Is 5^n < 0.04 ? Is 5^n < \frac{1}{25} ? Is 5^n < \frac{1}{5^2} ? Is 5^n < 5^{(-2)} ? Is n < -2 ? (1) (\frac{1}{5})^n > 25 --> \frac{1}{5^n} > 25 --> 5^n < \frac{1}{25} --> 5^n < 0.04 . Sufficient. (2) n^3 < n^2 --> n < 0 or 0 < n < 1 . Not sufficient. Answer: A.

WoundedTiger · Answer

Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2 Notice that for n\geq{0} so RHS of the Q stem is always greater than zero so we need to confirm whether n<-2 because 5^{-2} is 1/25 =0.04 St 1 says (1/5)^n > 25 or n>2 so st 1 is sufficient as n is positive St 2 says n^30 Case3 : 01 The expression will be true for all values Since, we have 2 ranges in which expression holds true and for those range n <-2 or n>-2.. Ans is A

Lucky2783 · Answer

Given 5^n < 0.04 5^n < 0.04 ( 0.04=4/100=1/25=5^{-2 } n<-2 ? option A: 5^{- n} > 25=5^2 ; implies n<-2 SUFFICIENT option B: n^3 < n^2 ==> n^3-n^2 <0 ==> n^2(n-1) <0 ==> n-1<0 ==> n<1 NOT SUFFICIENT. Bunuel , have i solved the second inequality incorrectly ? thanks lucky

Bunuel · Answer

Small correction: for (2) it should be n < 0 or 0 < n < 1. 0 must be excluded, because for n = 0, n^3 < n^2 does not hold true.

Lucky2783 · Answer

got it Bunuel . i missed it. thanks so much .

noTh1ng · Answer

Here is my approach: Statement 1: \frac{1}{5}^n > 25 5^-n > 5^2 -n > 2 n < -2 plug in n=-3 into the equation will yield that 1/125 is < than 0,04 Sufficient Statement 2: per statement n can be either a negative number or a proper fraction. 5^(1/2) would be > 0,04 while to a negative power would be <. not sufficient. --> A

KanishkM · Answer

Hi gmatbusters , Can you please share your thoughts on inline approach. Is this a validate approach ?? is 5^n < 5^-2 becomes is n < -2 ?? 1) 5^(-n) > 5^2 => -n > 2 => n < -2 Sufficient 2) Can't tell anything from this.

GMATBusters · Answer

Hii

Your approach to use first statement is correct.

For second statement.
n^3 < n^2
n^2(n-1)<0
n < 1
But since now n can be < or > -2, statement 2 is not sufficient

Hence Answer - A

AkshdeepS · Answer

Question : Is 5^n < 0.04 ? Or Is 5^n < \frac{4}{100} ? Or Is 5^n < 5^{-2} ? Finally, Is n < -2 ? Statement 1 : \frac{{1^n}}{{5}^n} > 25 Or 5 ^{-n} > 5^2 Or -n > 2 Or n < -2 (Answer to the question, YES) SUFFICIENT Statement 2 : n^3 < n^2 (As n^2 will always be positive, divide both sides by n^2) We get, n < 1 If n = 0 , the answer to the question is NO If n = - 3 , the answer to the question is YES NOT SUFFICIENT

CEdward · Answer

Pretty tricky.

Is 5^n < 0.04?

(1) (1/5)^n > 25
(2) n^3 < n^2

The question is asking 5^n < 0.04? This is the same as 5^n < 5^-2? In other words, is n less than -2?

(1) (1/5)^n > 25 ----> 5^-n > 5^2 ---> -n > 2 ---> n < -2
Sufficient.

(2) n^3 < n^2
n^3 - n^2 < 0
n^2 (n - 1) < 0 ---> Implies that n is negative, but n can be -1, -2, -3...Each of these satisfies the inequality.
Insufficient.

bumpbot · Answer

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Is 5^n < 0.04? (1) (1/5)^n > 25 (2) n^3 < n^2

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