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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]

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22 May 2003, 00:46
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Find an integer Q.

(1) Q^Q=Q^2
(2) sqrt Q=Q^2

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Manager
Joined: 28 Feb 2003
Posts: 99

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22 May 2003, 00:58
This is a beauty, I would go with C

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SVP
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22 May 2003, 01:12
Yes, C.
How do you find it? My copyright.

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Manager
Joined: 12 Oct 2003
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22 Dec 2003, 18:54
someone pls show working here ...

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Intern
Joined: 04 Oct 2003
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Location: Silicon Valley, CA

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22 Dec 2003, 20:47
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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Director
Joined: 13 Nov 2003
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22 Dec 2003, 20:54
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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Director
Joined: 13 Nov 2003
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23 Dec 2003, 07:53
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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Director
Joined: 03 Jul 2003
Posts: 651

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23 Dec 2003, 12:30
What is the value of 0^0?
Is it not zero?
If so, the answer shoud be E!

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Director
Joined: 13 Nov 2003
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23 Dec 2003, 12:31
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
Joined: 22 May 2003
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23 Dec 2003, 13:29
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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Director
Joined: 13 Nov 2003
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23 Dec 2003, 13:32
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
Joined: 22 May 2003
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23 Dec 2003, 13:38
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.

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Director
Joined: 13 Nov 2003
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23 Dec 2003, 13:44
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

http://www.cut-the-knot.org/htdocs/dcfo ... 49.shtml#1

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Senior Manager
Joined: 11 Nov 2003
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30 Dec 2003, 10:50
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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Senior Manager
Joined: 11 Nov 2003
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30 Dec 2003, 10:57
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

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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Director
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30 Dec 2003, 11:44
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

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.

Kudos [?]: 174 [0], given: 0

30 Dec 2003, 11:44
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