It is currently 19 Oct 2017, 06:00

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Apr 2012
Posts: 62

Kudos [?]: 75 [0], given: 21

Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)

### Show Tags

21 Jun 2012, 01:59
9
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

28% (00:57) correct 72% (00:59) wrong based on 297 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.
[Reveal] Spoiler: OA

Kudos [?]: 75 [0], given: 21

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [4], given: 12183

Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

21 Jun 2012, 02:17
4
KUDOS
Expert's post
6
This post was
BOOKMARKED
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.
_________________

Kudos [?]: 128837 [4], given: 12183

Manager
Joined: 27 Apr 2012
Posts: 62

Kudos [?]: 75 [0], given: 21

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, 03:10
This is great.Thanks a ton!

Kudos [?]: 75 [0], given: 21

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [0], given: 12183

Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

25 Jun 2013, 04:47
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

_________________

Kudos [?]: 128837 [0], given: 12183

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16681

Kudos [?]: 273 [0], given: 0

Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

04 Dec 2014, 05:14
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16681

Kudos [?]: 273 [0], given: 0

Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

26 Jan 2016, 06:57
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4133

Kudos [?]: 2891 [0], given: 0

GPA: 3.82
Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

27 Jan 2016, 18:46
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.

 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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 2891 [0], given: 0

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2212

Kudos [?]: 836 [0], given: 595

### Show Tags

09 Apr 2016, 23:47
IS 3^(A^2/B) <1 ?
[A] A<0
[B] B<0
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 836 [0], given: 595

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128837 [0], given: 12183

Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

10 Apr 2016, 01:16
stonecold wrote:
IS 3^(A^2/B) <1 ?
[A] A<0
[B] B<0

Merging topics. Please refer to the discussion above.
_________________

Kudos [?]: 128837 [0], given: 12183

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16681

Kudos [?]: 273 [0], given: 0

Re: Is 3^(a^2/b) < 1? [#permalink]

### Show Tags

17 Jun 2017, 03:55
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Re: Is 3^(a^2/b) < 1?   [#permalink] 17 Jun 2017, 03:55
Display posts from previous: Sort by