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If m and n are positive integers, is 4^m*(1/3)^n < 1? 19 Sep 2022, 05:28
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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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If m and n are positive integers, is 4^m*(1/3)^n < 1? 19 Sep 2022, 06:36
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Bunuel
If m and n are positive integers, is \(4^m*(\frac{1}{3})^n < 1\)?

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



Answer: Option A

Step-by-Step Video solution by GMATinsight

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If m and n are positive integers, is 4^m*(1/3)^n < 1? 19 Sep 2022, 11:46
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As the denominator is positive we can multiple both the sides by \(3^n\) without changing the signs.

Thus the question is asking us if

\(4^m < 3^n\)

Statement 1

n = 2m

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

\(4^m < 9^m\)

We know that m is a positive integer, hence the answer is a definite Yes

Hence this statement is sufficient.

Statement 2

We have information about n, but no information about m.

Hence the statement is not sufficient on its own.

Option A
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If m and n are positive integers, is 4^m*(1/3)^n < 1? 06 Apr 2023, 04:25
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Bunuel
If m and n are positive integers, is \(4^m*(\frac{1}{3})^n < 1\)?

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