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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
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20 Jul 2010, 01:38
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If m and n are positive, what is \(m * n\) ?
1. \(m^n = 1\)
2. \(n^m = 1\)
(C) 2008 GMAT Club - [t]m13#1[/t]
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
OE: Statement (1) by itself is insufficient. If m is 1, n can be any integer.
Statement (2) by itself is insufficient. If n is 1, m can be any integer.
Statements (1) and (2) combined are sufficient. From S1 and S2, it follows that \(m = n = 1\).
The correct answer is C.
--
As I think, we have one more option - when both m & n equals to 0.
Am I right?
1. \(m^n = 1\)
2. \(n^m = 1\)
(C) 2008 GMAT Club - [t]m13#1[/t]
Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient
Statements (1) and (2) TOGETHER are NOT sufficient
OE: Statement (1) by itself is insufficient. If m is 1, n can be any integer.
Statement (2) by itself is insufficient. If n is 1, m can be any integer.
Statements (1) and (2) combined are sufficient. From S1 and S2, it follows that \(m = n = 1\).
The correct answer is C.
--
As I think, we have one more option - when both m & n equals to 0.
Am I right?
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20 Jul 2010, 04:11
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In mathematics there are varying opinions on whether 0^0 equal 1 or whether it is undefined. The writers of the Gmat Club tests apparently assumed that 0^0 is undefined (hence choice C and not E).
This concept is not tested on the actual GMAT.
This concept is not tested on the actual GMAT.
