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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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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.
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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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GMAT Date: 06-11-2013
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Re: Is 3^(a^2/b) < 1? [#permalink]  21 Jun 2012, 02:10
This is great.Thanks a ton!
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Re: Is 3^(a^2/b) < 1? [#permalink]  25 Jun 2013, 03:47
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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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!

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Re: Is 3^(a^2/b) < 1? [#permalink]  26 Jan 2016, 05:57
Hello from the GMAT Club BumpBot!

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Re: Is 3^(a^2/b) < 1? [#permalink]  27 Jan 2016, 17:46
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

(1) a<0

(2) b<0

When you modify the original condition and the question, they become 3^(a^2/b) < 1? --> 3^(a^2/b) < 3^0? --> a^2/b>0?. Multiply b^2 on the both equations(since b^2 is positive, even if it’s multiplied, the sign of inequality doesn’t change.) and it becomes a^2(b)>0?. There are 2 variables(a,b), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), since a<0, it can’t be 0. Divide the both equations with a^2, they become a^2(b)<0?-->b<0?. Since 2) is b<0, it is yes and sufficient.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: Is 3^(a^2/b) < 1?   [#permalink] 27 Jan 2016, 17:46
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