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If u > 0 and v > 0, which is greater, u^v or v^u?
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16 Jun 2016, 03:17
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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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Re: If u > 0 and v > 0, which is greater, u^v or v^u?
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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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Re: If u > 0 and v > 0, which is greater, u^v or v^u?
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Updated on: 17 Jun 2016, 00:56
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?
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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?
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17 Jun 2016, 00:16
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



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Re: If u > 0 and v > 0, which is greater, u^v or v^u?
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04 Jul 2016, 01:13
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.



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Re: If u > 0 and v > 0, which is greater, u^v or v^u?
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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?
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04 Jul 2016, 01:45
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.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?
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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?
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04 Jul 2016, 03:01
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.
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Re: If u > 0 and v > 0, which is greater, u^v or v^u?
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04 Jul 2017, 05:35
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?
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10 Oct 2017, 20:04
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?



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