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# Is 3^(a^2/b) < 1?

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Is 3^(a^2/b) < 1? [#permalink]  21 Jun 2012, 00:59
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27% (01:58) correct 73% (00:53) wrong based on 167 sessions
Is 3^(a^2/b) < 1?

(1) a<0

(2) b<0

Hi, request your help to please understand the fundamental concept behind this question.
[Reveal] Spoiler: OA
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Re: Is 3^(a^2/b) < 1? [#permalink]  21 Jun 2012, 01:17
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Is 3^(a^2/b) < 1?

Notice that $$3^{\frac{a^2}{b}} < 1$$ to hold true, the power of 3 must be less than 0. So, the question basically asks whether $$\frac{a^2}{b}<0$$. This will happen if $$a\neq{0}$$ AND $$b<0$$ (if $$a=0$$ then $$\frac{a^2}{b}=0$$).

(1) a<0. The first condition is satisfied ($$a\neq{0}$$) but we don't know about the second one. Not sufficient.

(2) b<0. The second condition is satisfied ($$b<0$$) but we don't know about the first one (again if $$a=0$$ then $$\frac{a^2}{b}=0$$). Not sufficient.

(1)+(2) Both condition are satisfied. Sufficient.

For more on number theory and exponents check: math-number-theory-88376.html

DS questions on exponents: search.php?search_id=tag&tag_id=39
PS questions on exponents: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

Hope it helps.
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Manager
Joined: 27 Apr 2012
Posts: 62
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
Followers: 1

Kudos [?]: 24 [0], given: 21

Re: Is 3^(a^2/b) < 1? [#permalink]  21 Jun 2012, 02:10
This is great.Thanks a ton!
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Kudos [?]: 53616 [0], given: 8167

Re: Is 3^(a^2/b) < 1? [#permalink]  25 Jun 2013, 03:47
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Re: Is 3^(a^2/b) < 1? [#permalink]  04 Dec 2014, 04:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is 3^(a^2/b) < 1?   [#permalink] 04 Dec 2014, 04:14
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