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

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SVP
Joined: 03 Feb 2003
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Find an integer Q. (1) Q^Q=Q^2 (2) sqrt Q=Q^2 [#permalink]  21 May 2003, 23:46
Find an integer Q.

(1) Q^Q=Q^2
(2) sqrt Q=Q^2
Manager
Joined: 28 Feb 2003
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This is a beauty, I would go with C
SVP
Joined: 03 Feb 2003
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Kudos [?]: 77 [0], given: 0

Yes, C.
How do you find it? My copyright.
Senior Manager
Joined: 12 Oct 2003
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Location: USA
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someone pls show working here ...
Intern
Joined: 04 Oct 2003
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Location: Silicon Valley, CA
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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
Director
Joined: 13 Nov 2003
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Location: Florida
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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???
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
Director
Joined: 03 Jul 2003
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What is the value of 0^0?
Is it not zero?
If so, the answer shoud be E!
Director
Joined: 13 Nov 2003
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Kudos [?]: 33 [0], given: 0

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
Senior Manager
Joined: 22 May 2003
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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
Director
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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???
Senior Manager
Joined: 22 May 2003
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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.

Director
Joined: 13 Nov 2003
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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

http://www.cut-the-knot.org/htdocs/dcfo ... 49.shtml#1
Senior Manager
Joined: 11 Nov 2003
Posts: 355
Location: Illinois
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Kudos [?]: 0 [0], given: 0

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.
Senior Manager
Joined: 11 Nov 2003
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Location: Illinois
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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

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.
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 33 [0], given: 0

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

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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