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The three integers X, Y, and Z. Is their product XYZ = zero [#permalink]
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11 Sep 2006, 10:17
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The three integers X, Y, and Z. Is their product XYZ = zero
(1) X^Y=1
(2) X=Y=Z



Director
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Another good one
Think it is C)
From A) X=1, Y=1 or X=5,Y=0 then stem may be or may not be 0
B) by itself is not suffall three may be 0 or any other integer
From both when X=Y=Z=1 we get ans to question
C



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(E)
Statment 1:
X^Y=1 implies that
> X=1 and Y is any integer
or
> X is any integer and Y=0
Statment 2:
X=Y=Z brings nothing
(1) combined with (2)
X=Y=Z=1 works by giving 1^1=1
or
X=Y=Z=0 works by giving 0^0=1
So, it's insufficient.



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Re: Exponents [#permalink]
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11 Sep 2006, 10:50
yezz wrote: The three integers X, Y, and Z. Is their product XYZ = zero
(1) X^Y=1 (2) X=Y=Z
A it is
x^y=1
x^y=x^0
y=0 so xyz=0
or x=1!
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Director
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Hallo Fig,
Please confirm 0^0=1?



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I confirm
X^0=1 where X could be any real number



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Fig wrote: I confirm X^0=1 where X could be any real number
Any real number EXCEPT 0 0^0 is undefined , as is 0/0



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Answer: C
Q : Is XYZ = 0?
S1: X^Y = 1
Either X = 1 => X^Y =1 XYZ = YZ
or Y = 0 => XYZ = 0
Not sufficient.
S2: X=Y=Z
Could be anything.. Not sufficient.
S1 & S2:
X^Y = 1, if X = 1, XYZ = 1, Sufficient.
Y=0, XYZ = 0, Sufficient,
Answer: C



Manager
Joined: 01 Jun 2006
Posts: 139

E in my opinion if consider 0^0=1
But if consider 0^0=0 so we got x,y,z must be equal 1 and xyz<>0 so C it is.
Plz post OA yezz



Director
Joined: 23 Jun 2005
Posts: 841

Same dilemma as everyone else. Vote for E



Intern
Joined: 27 Aug 2006
Posts: 18

Got the following from the purpulemath exponent chapter.
http://purplemath.com/modules/exponent2.htm
Another comment: Please don't ask me to "define" 00. There are at least two ways of looking at this quantity:
* Anything to the zero power is "1", so 0^0 = 1.
* Zero to any power is zero, so 0^0 = 0.
As far as I know, the "math gods" have not yet settled on a "definition" of 00. In fact, in calculus, "00" will be called an "indeterminant form". If this quantity comes up on class, don't assume: ask your instructor what you should do with it.
I would go w/ E as it's not clear what's the value of 0^0.



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frommirage wrote: If this quantity comes up on class, don't assume: ask your instructor what you should do with it.
Kevincan is a Kaplan instructor(with 780 score) and he has already confirmed that 0^0 is undefined. (See his post above)
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I maintain my point of view It's a result very specific and famous for it
To the ones that doubt, i suggest that they use the window calculator for example. They can calculate 0^0=1.... The result is 1
And to be sure, they can try:
> 1,2^2,1 >>>> Invalid input function
> 1/0 >>>> cannot divid by zero
In addition, this result is required for a "Serie" representing a fonction. For the ones who remind it, we have
f(x)= Sigma( a(k)*x^k ) where k start from 0 and tend to infinate.
We can imagine imagine a fonction defined for a the value of x=0 thus
f(0) = a(0)*0^0 = a(0)
Last edited by Fig on 12 Sep 2006, 03:10, edited 3 times in total.



VP
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C is right. 0^0 is invalid math expression. they can only be 1.



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Fig wrote: I maintain my point of view It's a result very specific and famous for it To the ones that doubt, i suggest that they use the window calculator for example. They can calculate 0^0=1.... The result is 1 And to be sure, they can try: > 1,2^2,1 >>>> Invalid input function > 1/0 >>>> cannot divid by zero In addition, this result is required for a "Serie" representing a fonction. For the ones who remind it, we have f(x)= Sigma( a(k)*x^k ) where k start from 0 and tend to infinate. We can imagine imagine a fonction defined for a the value of x=0 thus f(0) = a(0)*0^0 = a(0)
Don't be confused. Windows calculator is not a maths standard. Windows did not design calculator to clarify the math fundamentals. See the below link. It is clearly stated that "A number other than 0 taken to the power 0 is defined to be 1"
http://mathworld.wolfram.com/Power.html
NOTE: This is one of the trusted link.
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Interesting link The content does not state on 0^0.
Moreover, concerning calculators, I have tried on 3 differents, one of them is my old HP 48S confirmed it ... Excell works on it too... and so on Windows calculator is just a common and easytoaccess calculator
I personnaly practiced, well a few time ago, some math problems involving 0^0. As i said, a 'serie' represating a fonction is one application.
Some examples:
> f(x) = a0 + a1*x
= Sigma ( a(k)*x^k)
= a(0)*X^0+a(1)*X^1
Thus, F(0) = a(0)*0^0+a(1)*0^1 = a(0)
> f(x) = a0 + a1*x + a2*x^2
= Sigma ( a(k)*x^k)
= (0)*X^0+a(1)*X^1+a(2)*X^2
Thus, F(0) = a(0)*0^0+a(1)*0^1+a(2)*0^2 = a(0)
We can definie sin(), cos() etc... by Sigma ( a(k)*x^k) with k starting at 0
Sorry for it, this is a french link presenting famous series in application for physics:
http://www.sciences.univnantes.fr/physique/perso/blanquet/conducti/a1besleg/a1besleg.htm
U can notice that k starts at 0 in



Director
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great discussion but whats the OA?
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THANKS EVERYONE, C is correct OA
(1) X^Y=1 follows that 1^1=1, 0^1=1, and â€“1^0=1: NOT ENOUGH
(2) is of no use
combine , X=Y=Z=1, so the product does not equal to a zero.
thus, C.



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CEO
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Fig wrote:
Fig,
Don't rely on calculators but rely on math theorems.
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