GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Dec 2018, 21:55

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $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
Manager
avatar
Joined: 27 Apr 2012
Posts: 57
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
GMAT ToolKit User Premium Member
Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 21 Jun 2012, 00:59
1
15
00:00
A
B
C
D
E

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
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Manager
Manager
avatar
Joined: 27 Apr 2012
Posts: 57
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
GMAT ToolKit User Premium Member
Re: Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 21 Jun 2012, 02:10
This is great.Thanks a ton!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 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"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Intern
avatar
B
Joined: 09 Apr 2018
Posts: 12
CAT Tests
Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 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.

Answer: C.

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
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: Is 3^(a^2/b) < 1?  [#permalink]

Show Tags

New post 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.

Answer: C.

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: Is 3^(a^2/b) < 1? &nbs [#permalink] 25 Oct 2018, 06:17
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.