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

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Math Expert
Joined: 02 Sep 2009
Posts: 60480
If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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16 Jun 2016, 03:17
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5% (low)

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85% (01:07) correct 15% (01:30) wrong based on 1237 sessions

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

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

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Joined: 16 Aug 2015
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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16 Jun 2016, 21:01
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.
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Community Reply Manager Joined: 21 Sep 2015 Posts: 73 Location: India GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41 Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags Updated on: 17 Jun 2016, 00:56 8 2 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 Originally posted by rishi02 on 16 Jun 2016, 07:04. Last edited by rishi02 on 17 Jun 2016, 00:56, edited 1 time in total. ##### General Discussion Intern Joined: 30 Jun 2014 Posts: 35 GPA: 3.6 WE: Operations (Energy and Utilities) Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 16 Jun 2016, 07:13 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. Manager Joined: 18 Jan 2010 Posts: 238 Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 17 Jun 2016, 00:16 1 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 Current Student Joined: 04 Feb 2014 Posts: 215 Location: India Concentration: General Management, Entrepreneurship GPA: 3 WE: Project Management (Manufacturing) Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 04 Jul 2016, 01:13 1 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. Current Student Joined: 04 Feb 2014 Posts: 215 Location: India Concentration: General Management, Entrepreneurship GPA: 3 WE: Project Management (Manufacturing) Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 04 Jul 2016, 01:14 Bunuel Can you please post the OA? Looks tricky. IMO B should be the answer. Can anyone solve it by picking up the numbers? Math Expert Joined: 02 Sep 2009 Posts: 60480 Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 04 Jul 2016, 01:45 1 anurag16 wrote: Bunuel Can you please post the OA? Looks tricky. IMO B should be the answer. Can anyone solve it by picking up the numbers? The OA is C. Please refer to the solutions above and ask if anything remains unclear. _________________ Current Student Joined: 04 Feb 2014 Posts: 215 Location: India Concentration: General Management, Entrepreneurship GPA: 3 WE: Project Management (Manufacturing) Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 04 Jul 2016, 01:50 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. Math Expert Joined: 02 Sep 2009 Posts: 60480 Re: If u > 0 and v > 0, which is greater, u^v or v^u? [#permalink] ### Show Tags 04 Jul 2016, 03:01 1 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. _________________ SVP Joined: 26 Mar 2013 Posts: 2346 Concentration: Operations, Strategy Schools: Erasmus '21 (M$)
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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04 Jul 2017, 05:35
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

Manager
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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]

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10 Oct 2017, 20:04
1
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?
Manager
Joined: 11 Sep 2019
Posts: 77
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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14 Dec 2019, 04:25
MathRevolution wrote:
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.

What is this? I did not understand it at all. Please elaborate. The method seems tactful but I am not getting the same
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Posts: 1001
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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14 Dec 2019, 09:21
Bunuel wrote:
If u > 0 and v > 0, which is greater, $$u^v$$ or $$v^u$$?

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

$$u^v$$ ?? $$v^u$$

Statement 1 : u=1

$$1^v$$ ?? $$v^1$$

Since we don't know anything about v (except it is positive) statement 1 is insufficient.

Statement 1 : v>2. Let's say 3

$$u^3$$ ?? $$3^u$$

Since we don't know anything about u (except it is positive) statement 2 is insufficient.

Combined :

$$1^3$$ < $$3^1$$

Hence Sufficient.

Note: Even if you take value of v as 2.5, the relation will still hold true.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?   [#permalink] 14 Dec 2019, 09:21
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