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Re: If m and n are positive integers, is 4^m*(1/3)^n < 1? [#permalink]
Expert Reply
Bunuel wrote:
If m and n are positive integers, is \(4^m*(\frac{1}{3})^n < 1\)?

(1) n = 2m
(2) n = 4


 


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Official Solution:


If \(m\) and \(n\) are positive integers, is \(4^m*(\frac{1}{3})^n < 1\)?

First, let's simplify the question:

Is \(4^m*\frac{1}{3^n} < 1\)?

Is \(4^m < 3^n\)?

(1) \(n = 2m \)

Substituting \(n = 2m\) into the question, it becomes:

Is \(4^m < 3^{2m}\)?

Is \(4^m < 9^{m}\)?

Since given that \(m\) is a positive integer, the answer to this question is YES. Sufficient.

(2) \(n = 4\)

Substituting \(n = 4\) into the question, it becomes:

Is \(4^m < 3^4\)?

Is \(4^m < 81\)?

If \(m=1\), the answer is YES. However, if \(m = 100\), the answer is NO. Not sufficient.


Answer: A
GMAT Club Bot
Re: If m and n are positive integers, is 4^m*(1/3)^n < 1? [#permalink]
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