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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # Is 3^(a^2/b) < 1?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Joined: 27 Apr 2012 Posts: 57 Location: United States GMAT Date: 06-11-2013 GPA: 3.5 WE: Marketing (Consumer Products) Is 3^(a^2/b) < 1? [#permalink] ### Show Tags 21 Jun 2012, 00:59 1 15 00:00 Difficulty: 95% (hard) Question Stats: 32% (00:58) correct 68% (01:01) wrong based on 378 sessions ### HideShow timer Statistics 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. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Is 3^(a^2/b) < 1? [#permalink] ### Show Tags 21 Jun 2012, 01:17 7 6 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. Answer: C. 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. _________________ ##### General Discussion Manager Joined: 27 Apr 2012 Posts: 57 Location: United States GMAT Date: 06-11-2013 GPA: 3.5 WE: Marketing (Consumer Products) Re: Is 3^(a^2/b) < 1? [#permalink] ### Show Tags 21 Jun 2012, 02:10 This is great.Thanks a ton! Math Expert Joined: 02 Sep 2009 Posts: 51218 Re: Is 3^(a^2/b) < 1? [#permalink] ### Show Tags 25 Jun 2013, 03:47 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is 3^(a^2/b) < 1? [#permalink] ### Show Tags 27 Jan 2016, 17:46 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. Therefore, the answer is C.  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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Joined: 09 Apr 2018
Posts: 12

### Show Tags

25 Oct 2018, 05:33
Bunuel wrote:
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: http://gmatclub.com/forum/math-number-theory-88376.html

DS questions on exponents: http://gmatclub.com/forum/search.php?se ... &tag_id=39
PS questions on exponents: http://gmatclub.com/forum/search.php?se ... &tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: http://gmatclub.com/forum/tough-and-tri ... 25967.html
Tough and tricky PS exponents and roots questions with detailed solutions: http://gmatclub.com/forum/tough-and-tri ... 25956.html

Hope it helps.

Bunuel ...if a=-1 and b=-9 then we get 3 as our answer and if a=-1 and b=-2 in that case we get .66
Should the answer not be E.
Math Expert
Joined: 02 Sep 2009
Posts: 51218
Re: Is 3^(a^2/b) < 1?  [#permalink]

### Show Tags

25 Oct 2018, 06:17
angarg wrote:
Bunuel wrote:
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: http://gmatclub.com/forum/math-number-theory-88376.html

DS questions on exponents: http://gmatclub.com/forum/search.php?se ... &tag_id=39
PS questions on exponents: http://gmatclub.com/forum/search.php?se ... &tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: http://gmatclub.com/forum/tough-and-tri ... 25967.html
Tough and tricky PS exponents and roots questions with detailed solutions: http://gmatclub.com/forum/tough-and-tri ... 25956.html

Hope it helps.

Bunuel ...if a=-1 and b=-9 then we get 3 as our answer and if a=-1 and b=-2 in that case we get .66
Should the answer not be E.

If a=-1 and b=-9, then 3^(1/(-9)) = ~0.9.
_________________
Re: Is 3^(a^2/b) < 1? &nbs [#permalink] 25 Oct 2018, 06:17
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