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May 0510:00 AM PDT
-11:00 AM PDT
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.
23 Jan 2012, 21:09
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Is \(a^b \gt b^a\) ?
1. \(a \gt b \gt 1\)
2. \(a = b + 1\)
* 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
Ans (E)
Can someone please provide suitable set of numbers for testing these statements? I used number testing approach but had a hard time coming up with the right set of numbers? How do you figure what type of numbers should you be testing for these types of questions?
1. \(a \gt b \gt 1\)
2. \(a = b + 1\)
* 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
Ans (E)
Can someone please provide suitable set of numbers for testing these statements? I used number testing approach but had a hard time coming up with the right set of numbers? How do you figure what type of numbers should you be testing for these types of questions?
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24 Jan 2012, 03:40
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teal
On DS questions when plugging numbers, your goal is to prove that the statement is not sufficient. So you should try to get an YES answer with one chosen number(s) and a NO with another.
Is \(a^b \gt b^a\) ?
(1) \(a \gt b \gt 1\) --> first try minimum possible integers for \(a\) and \(b\): if \(a=3\) and \(b=2\) then \(a^b=9>8=b^a\) and the answer is YES. Now, increase \(a\) and \(b\) and try: \(a=4\) and \(b=3\) then \(a^b=64<81=b^a\), so in this case the answer is NO.
(2) \(a = b + 1\). The same set of numbers works for this statement as well. Not sufficient.
(1)+(2) Again, two sets of numbers considered, satisfy both statements and give different answer to the question. Not sufficient.
Hope it's clear.
26 Jan 2012, 15:39
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Thanks a lot, Bunuel!
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Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests
for the latest questions.
Still interested? Check out the "Best Topics" block above for better discussion and related questions.
Thank you for understanding, and happy exploring!
