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Prolbem old problem

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Prolbem old problem [#permalink] New post 18 May 2003, 21:52
Expert's post
I have been working on the question bank lately and found a problematic question here. It was posted by Stolyar a while ago.

Find an integer J.

(1) [J]=J^-1
(2) J^J=1

[...] is absolute value


The answer back then was ruled D.

Is 0^0=1 or is it undefined? I think somebody brought this one up lately. Can anybody help?


BBbbb
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Re: Prolbem old problem [#permalink] New post 18 May 2003, 23:21
bb wrote:
I have been working on the question bank lately and found a problematic question here. It was posted by Stolyar a while ago.

Find an integer J.

(1) [J]=J^-1
(2) J^J=1

[...] is absolute value


The answer back then was ruled D.

Is 0^0=1 or is it undefined? I think somebody brought this one up lately. Can anybody help?


BBbbb



J^J=1 -- the only integer that satisfies is 1. 0^0 is not always =1; thus it has to be eliminated.
Expert Post
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Re: Prolbem old problem [#permalink] New post 19 May 2003, 09:56
Expert's post
stolyar wrote:
bb wrote:
I have been working on the question bank lately and found a problematic question here. It was posted by Stolyar a while ago.

Find an integer J.

(1) [J]=J^-1
(2) J^J=1

[...] is absolute value


The answer back then was ruled D.

Is 0^0=1 or is it undefined? I think somebody brought this one up lately. Can anybody help?


BBbbb



J^J=1 -- the only integer that satisfies is 1. 0^0 is not always =1; thus it has to be eliminated.



:hair What do you mean it is not always 1?
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 [#permalink] New post 19 May 2003, 21:18
Well, it depends on a function. Different functions give different answers.

f(x)=x^x for x=0
f(x)=(x-3)^(x-3) for x=3
f(x)=(x^2)^x for x=0

there are many functions that give 0^0 in some particular cases. Sometimes 0^0=1, other times infinity, still other times it does not exist.

such problems are to be solved by using difficult math analysis -- a derivative function or a prime function, which are NOT GMAT subjects.
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 [#permalink] New post 20 May 2003, 07:53
hi guys im confused ...can u clarify how J*J=1 for 1 only.

if J*J=1 , J=+/-1 both satisfy it.
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GMAT 1: 750 Q49 V42
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Kudos [?]: 9415 [0], given: 3699

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 [#permalink] New post 20 May 2003, 12:10
Expert's post
arun wrote:
hi guys im confused ...can u clarify how J*J=1 for 1 only.

if J*J=1 , J=+/-1 both satisfy it.


if J is -1 then you will get (-1)^(-1), which equals to 1/(-1), whic is -1, that is negative. It is not J*J, it is J^J
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 [#permalink] New post 20 May 2003, 21:05
Yeah... People confuse multiplication with raising into a power and vice versa
  [#permalink] 20 May 2003, 21:05
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