• Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

If u > 0 and v > 0, which is greater

This topic has 3 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

If u > 0 and v > 0, which is greater

Post Mon Jul 24, 2017 9:28 am
If u > 0 and v > 0, which is greater, u^v or v^u?
(1) u = 1
(2) v > 2

Official Guide question
Answer: C

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Post Fri Dec 08, 2017 6:55 am
jjjinapinch wrote:
If u > 0 and v > 0, which is greater, u^v or v^u?
(1) u = 1
(2) v > 2
We are given that u > 0 and that v > 0. We must determine whether u^v is greater than v^u.

Statement One Alone:

u = 1

If u = 1, then u^v = 1^v = 1 (recall that 1 raised to any power is 1) and v^u = v^1 = v (recall that any number raised to the 1st power is itself). However, since we do not know the value of v, we cannot determine whether u^v is greater than v^u.

For example, if v = 2, then u^v < v^u (1^2 < 2^1). However, if v = ½, then u^v > v^u because 1^(1/2) > (1/2)^1. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

v > 2

Although we know that v > 2, since we do not have any information about u, we cannot answer the question. Statement two alone is not sufficient. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that u = 1 and that v > 2. Thus, we see that:

u^v = 1^v = 1 and v^u > 2^1 (since v > 2). Since v^u > 2 and u^v = 1, v^u is greater than u^v.

Answer: C

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Mon Jul 24, 2017 5:27 pm
Hi jjjinapinch,

This question can be solved by TESTing VALUES.

We're told that both U and V are POSITIVE (and while that doesn't necessarily mean that they have to be positive integers, we can use integers to get to the correct answer). We're asked whether U^V or V^U is greater. This is the equivalent of a YES/NO question.

1) U = 1

IF.....
V = 1
then 1^1 and 1^1 are the SAME value, so NEITHER is greater.

IF....
V = 2
then 1^2 = 1 and 2^1 = 2, so V^U is greater.
Fact 1 is INSUFFICIENT

2) V > 2

IF....
V = 3, U = 1
then 1^3 = 1 and 3^1 = 3, so V^U is greater.

IF....
V = 3, U = 3
then 3^3 and 3^3 are the SAME value, so NEITHER is greater.
Fact 1 is INSUFFICIENT

Combined, we know....
U = 1 and V > 2
U^V will always be 1^(something > 2) = 1 and V^U = (something greater than 2)^1 = that same value greater than 2. Thus, V^U will ALWAYS be greater.
Combined, SUFFICIENT

Final Answer:
C

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Ian Stewart GMAT Instructor
Joined
02 Jun 2008
Posted:
2285 messages
Followed by:
346 members
Upvotes:
1090
GMAT Score:
780
Post Mon Jul 24, 2017 5:07 pm
Using Statement 1, if u = 1, then

u^v = 1^v = 1

and

v^u = v^1 = v

So the question "which is greater, u^v or v^u?" becomes "which is greater, 1 or v?" We don't know if v is greater than 1 (we only know that v > 0) so Statement 1 is not sufficient. But when we use both statements, we know v > 2, so v is certainly greater than 1, and the answer is C.

Statement 2 is not sufficient alone. We just saw above that v^u can be larger, but using only statement 2, it might be that u = 3 and v = 3, say, and then neither of u^v or v^u is larger than the other, so we can get two different answers to the question only using Statement 2. Other sets of values will prove that as well - I think the OG solution uses u = 3 and v = 4.

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 174 topics
2 lheiannie07 110 topics
3 ardz24 64 topics
4 LUANDATO 56 topics
5 swerve 46 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

150 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

145 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
4 image description GMATGuruNY

The Princeton Review Teacher

103 posts
5 image description Scott@TargetTestPrep

Target Test Prep

98 posts
See More Top Beat The GMAT Experts