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SVP
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Find an integer Q. (1) Q^Q=Q^2 (2) sqrt Q=Q^2 [#permalink]
 22 May 2003, 00:46
Find an integer Q. 
(1) Q^Q=Q^2
(2) sqrt Q=Q^2
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Manager
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This is a beauty, I would go with C
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SVP
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Yes, C.
How do you find it? My copyright.
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Senior Manager
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someone pls show working here ...
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Intern
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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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VP
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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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Director
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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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Director
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What is the value of 0^0?
Is it not zero?
If so, the answer shoud be E!
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VP
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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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Senior Manager
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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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VP
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stolyar wrote: Yes, C. How do you find it? My copyright. pls, explain. furnish the copyrighted items.
Q^Q=Q^2
Q=2 ... ??? what's wrong with this???
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Senior Manager
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dj wrote: stolyar wrote: Yes, C. How do you find it? My copyright. 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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VP
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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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Senior Manager
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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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Senior Manager
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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#1I 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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VP
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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#1I 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!
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close
