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Find an integer Q. (1) Q^Q=Q^2 (2) sqrt Q=Q^2

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Find an integer Q. (1) Q^Q=Q^2 (2) sqrt Q=Q^2 [#permalink] New post 21 May 2003, 23:46
Find an integer Q. :saw

(1) Q^Q=Q^2
(2) sqrt Q=Q^2
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 [#permalink] New post 21 May 2003, 23:58
This is a beauty, I would go with C
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 [#permalink] New post 22 May 2003, 00:12
Yes, C.
How do you find it? My copyright.
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 [#permalink] New post 22 Dec 2003, 17:54
someone pls show working here ...
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 [#permalink] New post 22 Dec 2003, 19:47
a) to possible values 1 and 2

b) to possile values 0 and 1

then taking them together => 1

Ans -C
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 [#permalink] New post 22 Dec 2003, 19:54
bat_car wrote:
a) to possible values 1 and 2

b) to possile values 0 and 1

then taking them together => 1

Ans -C


in A, the base is same, Q, so the exponent should be equal? ain't it?

Q^Q=Q^2
Q=2 ... ??? what's wrong with this???
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 [#permalink] New post 23 Dec 2003, 06:53
From 1) Q can be 1 or 2 , 1^1=1^2=1; Q=2, 2^2=2^2=4 so 1) insufficient
From 2) sqrtQ=Q^2 so square both sides Q-Q^4=0 or Q(1-Q^3)=0 so Q=0, or Q=1 , 2) is also insufficient, so from both Q=1
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 [#permalink] New post 23 Dec 2003, 11:30
What is the value of 0^0?
Is it not zero?
If so, the answer shoud be E!
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 [#permalink] New post 23 Dec 2003, 11:31
kpadma wrote:
What is the value of 0^0?
Is it not zero?
If so, the answer shoud be E!


this is still controversial. anyhow, for the calculation sake you can take it as 1
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 [#permalink] New post 23 Dec 2003, 12:29
kpadma wrote:
What is the value of 0^0?
Is it not zero?
If so, the answer shoud be E!


isn't 0^0 undetermined? like for instance 1/0?

in that case answer is still E
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 [#permalink] New post 23 Dec 2003, 12:32
stolyar wrote:
Yes, C.
How do you find it? My copyright.
:flower


pls, explain. furnish the copyrighted items.

Q^Q=Q^2
Q=2 ... ??? what's wrong with this???
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 [#permalink] New post 23 Dec 2003, 12:38
dj wrote:
stolyar wrote:
Yes, C.
How do you find it? My copyright.
:flower


pls, explain. furnish the copyrighted items.

Q^Q=Q^2
Q=2 ... ??? what's wrong with this???



As others already explained above, Q^Q=Q^2 works for both Q=2 and Q=1 (1^1=1^2=1)

I think the issue here is whether we should consider 0^0 as 0,1 or undetermined.


comments?
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 [#permalink] New post 23 Dec 2003, 12:44
I really understand that. But do we need to go this far, taking in cosideration so many things and assumptions?

basic mathematics says: if the base is same, then exponent/power is equal. doesn't this answer the question?

or, we need to dissect everything in all possible ways?

anyway, 0^0 is 1, I think we discussed this in one of the chat thread. I don't know which. ..for calculation purposes only..try windows CALC

read this thread, anyway.
http://www.cut-the-knot.org/htdocs/dcfo ... 49.shtml#1
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 [#permalink] New post 30 Dec 2003, 09:50
I think 0^0 is undefined term. But this is very controversial and no common agreement prevail even among mathematician. So I think ETS will never devise a quetsion that are controvercial.

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

Nevertheless, for the purpose of this problem, I will go for C.
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 [#permalink] New post 30 Dec 2003, 09:57
dj wrote:
I really understand that. But do we need to go this far, taking in cosideration so many things and assumptions?

basic mathematics says: if the base is same, then exponent/power is equal. doesn't this answer the question?

or, we need to dissect everything in all possible ways?

anyway, 0^0 is 1, I think we discussed this in one of the chat thread. I don't know which. ..for calculation purposes only..try windows CALC

read this thread, anyway.
http://www.cut-the-knot.org/htdocs/dcfo ... 49.shtml#1


I think the basic mathemetics definition you are referring to applies only when the base is NOT a variable. So according to basic mathematics, if 5^n = 5^2, then n=2 But if Q^Q = Q^2, then we can not conclude that Q = 2.
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 [#permalink] New post 30 Dec 2003, 10:44
gmatblast wrote:
dj wrote:
I really understand that. But do we need to go this far, taking in cosideration so many things and assumptions?

basic mathematics says: if the base is same, then exponent/power is equal. doesn't this answer the question?

or, we need to dissect everything in all possible ways?

anyway, 0^0 is 1, I think we discussed this in one of the chat thread. I don't know which. ..for calculation purposes only..try windows CALC

read this thread, anyway.
http://www.cut-the-knot.org/htdocs/dcfo ... 49.shtml#1


I think the basic mathemetics definition you are referring to applies only when the base is NOT a variable. So according to basic mathematics, if 5^n = 5^2, then n=2 But if Q^Q = Q^2, then we can not conclude that Q = 2.


got your point..thanks!
  [#permalink] 30 Dec 2003, 10:44
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