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

It is currently 17 Nov 2018, 05:11

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     November 18, 2018

     November 18, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

If u > 0 and v > 0, which is greater, u^v or v^u?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50621
If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 16 Jun 2016, 02:17
2
11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (00:49) correct 16% (01:10) wrong based on 933 sessions

HideShow timer Statistics

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 21 Sep 2015
Posts: 78
Location: India
GMAT 1: 730 Q48 V42
GMAT 2: 750 Q50 V41
Reviews Badge
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post Updated on: 16 Jun 2016, 23:56
7
1
If u > 0 and v > 0, which is greater, u^v or v^u?

(1) u = 1

Since we are not told if u and v are different numbers there are two possibilites:
a) u=v= 1 in which case u^v = v^u
b) They are different numbers in which case v^u will always be greater since u^v = 1 (1 raised to anything is 1)

(2) v > 2

It does not give us any information about u. For example u could be 3 and v could be 4 and vice versa

On combining we know u^v will always be 1 . Therefore v^u is greater. SUFFICIENT

Ans = C
_________________

Appreciate any KUDOS given ! :)


Originally posted by rishi02 on 16 Jun 2016, 06:04.
Last edited by rishi02 on 16 Jun 2016, 23:56, edited 1 time in total.
General Discussion
Intern
Intern
avatar
B
Joined: 30 Jun 2014
Posts: 42
GPA: 3.6
WE: Operations (Energy and Utilities)
GMAT ToolKit User
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 16 Jun 2016, 06:13
from statement 1) u=1 so, (1)^v= 1 and v^1. if v=1 then both are equal otherwise v^1 > 1^v. so not sufficient.
2) statement 2. not sufficient. as we know the value of v only.

1) +2) sufficient because this will eliminate the first case when v=1 from first statement.
answer C.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 16 Jun 2016, 20:01
The original condition has 2 variables, so we need 2 variables as well. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer.
Attachments

variable approach's answer probability.jpg
variable approach's answer probability.jpg [ 219.74 KiB | Viewed 6870 times ]


_________________

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"

Senior Manager
Senior Manager
User avatar
Joined: 18 Jan 2010
Posts: 252
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 16 Jun 2016, 23:16
Bunuel wrote:
If u > 0 and v > 0, which is greater, u^v or v^u?

(1) u = 1
(2) v > 2


Statement 1
when u = 1, u raised to any power is always 1. Also v^u is always v.

If v>1 then v^u > u^v

If v[b]<1, then v^u < u^v [/b]

Clearly not sufficient.

Statement 2

v > 2

say u = 0.5

(3)^0.5 = 1.732
(0.5)^3 = 0.125

v^u > u^v


v=4; u=-1

v^u = 4^(-1) = (1/4)
u^v = (-1)^4 =1

v^u < u^v

Not sufficient.

Combining these two.
v > 2; u = 1
when u = 1, u raised to any power is always 1. Also v^u is always v.

since v is always > 2, and u is always 1. hence

v^u is always greater than u^v
Manager
Manager
User avatar
G
Joined: 04 Feb 2014
Posts: 245
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3
WE: Project Management (Manufacturing)
GMAT ToolKit User
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 04 Jul 2016, 00:13
adiagr According to ques u>0 so it should not be taken as -1

adiagr wrote:
Statement 2 v > 2 say u = 0.5(3)^0.5 = 1.732(0.5)^3 = 0.125v^u > u^v v=4; u=-1v^u = 4^(-1) = (1/4) u^v = (-1)^4 =1 v^u < u^v Not sufficient.

_________________

Kudos if you like my post

Manager
Manager
User avatar
G
Joined: 04 Feb 2014
Posts: 245
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3
WE: Project Management (Manufacturing)
GMAT ToolKit User
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 04 Jul 2016, 00:14
Bunuel Can you please post the OA?

Looks tricky. IMO B should be the answer.

Can anyone solve it by picking up the numbers?
_________________

Kudos if you like my post

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50621
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 04 Jul 2016, 00:45
Manager
Manager
User avatar
G
Joined: 04 Feb 2014
Posts: 245
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3
WE: Project Management (Manufacturing)
GMAT ToolKit User
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 04 Jul 2016, 00:50
Bunuel Thanks for your reply.

In statement 2:

u=1 and v=3 Then v^u is greater
u=4 and v=3 Then v^u is greater

Please tell a situation when it will not hold true.
_________________

Kudos if you like my post

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50621
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 04 Jul 2016, 02:01
anurag16 wrote:
Bunuel Thanks for your reply.

In statement 2:

u=1 and v=3 Then v^u is greater
u=4 and v=3 Then v^u is greater

Please tell a situation when it will not hold true.


You can consider the case when u = v. In this case v^u is NOT greater than u^v.
_________________

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

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1880
Reviews Badge CAT Tests
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 04 Jul 2017, 04:35
1
If u > 0 and v > 0, which is greater, u^v or v^u?

(1) u = 1

Let v = 10........then 1^10 < 10^1

Let v= 1...........then 1^1 = 1^1

Insufficient

(2) v > 2

same example as above:
Let v = 10........then 1^10 < 10^1

Let v= 10...........then 10^10 = 10^10

Insufficient

Combine 1 & 2

V > 2 & u= 1..........So first example applies

Let v = 10........then 1^10 < 10^1

Sufficient

Answer: C
Senior Manager
Senior Manager
avatar
G
Joined: 26 Dec 2015
Posts: 258
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 10 Oct 2017, 19:04
i know this says its a <600 level problem, but i could not disagree more. is it just me or does this seem to be at least 600 level?
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8801
Premium Member
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

Show Tags

New post 22 Oct 2018, 03:14
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If u > 0 and v > 0, which is greater, u^v or v^u? &nbs [#permalink] 22 Oct 2018, 03:14
Display posts from previous: Sort by

If u > 0 and v > 0, which is greater, u^v or v^u?

  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®.