If n is an integer such that (-3)^(-4n) 3^(6 - n), which of the

Question

If n is an integer such that  (-3)^{-4n} > 3^{6-n} , which of the following must be true?

I. n is even
II. n is not a prime number
III. n < 3

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

IanStewart · Accepted Answer

In the inequality

(-3)^{-4n} > 3^{6-n}

we're raising the left side to an even power, so it's going to become positive in the end, and we can ignore the negative sign. Once we do that, we have equal positive integer bases on both sides (and our bases are greater than 1), and the left side will exceed the right precisely when the exponent on the left exceeds the exponent on the right. So

-4n > 6 - n
-6 > 3n
-2 > n

So n is definitely negative here, so cannot be prime, and is certainly less than 3. So II and III must be true. There's no way to tell if n is even, however. So D is the answer.

nick1816 · Answer

(-3)^{-4n} > 3^{6-n} 3^{-4n} > 3^{6-n} .... AS -4n is even. Since 3^x is an increasing function -4n > 6-n -3n > 6 n<-2 I) n can be -3. Hence I can be false . II) n is negative. Hence, n can never be a prime number. Must be true III) n<-2 <3 Must be true D

mSKR · Answer

(−3)^-4n > 3^(6-n)
to make LHS greated

1. n also need to be -ve so that -3 stays in numerator
3. if both side |3| is common then -4n must be greater than 6-n
-4n>6-n
-3n>6
n<-2 and n has to be negative so n <-2

I. n has to be even ; if n=-3 still result hold true : n can be even or odd-FALSE
II. n is not a prime number; TRUE( all numbers below -2 can not be prime number)-TRUE
III. n has to be less than -2 ; it means it is always less than n<3

hence D

thr3at · Answer

Hello  IanStewart ,

N is definetly <0 ,
III says N < 3 ( this inlcudes 0,1,2) then III must not be True.

Am I missing something here? Please explain.

Bunuel · Answer

(-3)^{-4n} > 3^{6-n}  implies that n must be a negative integer. For any negative integer, it would be true to say that it's less than 3. So, whatever n is, it's for sure less than 3. Thus, III is always true.

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If n is an integer such that (-3)^(-4n) > 3^(6 - n), which of the

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