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

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

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New post 16 Jun 2016, 03:17
3
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

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

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

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New post 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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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post Updated on: 17 Jun 2016, 00:56
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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.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 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.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 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
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 04 Jul 2016, 01:13
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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.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 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?
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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

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New post 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.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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

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New post 04 Jul 2017, 05:35
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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
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 10 Oct 2017, 20:04
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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?
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 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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Re: If u > 0 and v > 0, which is greater, u^v or v^u?  [#permalink]

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New post 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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