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# The three integers X, Y, and Z. Is their product XYZ = zero

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The three integers X, Y, and Z. Is their product XYZ = zero [#permalink]  11 Sep 2006, 09:17
The three integers X, Y, and Z. Is their product XYZ = zero

(1) X^Y=1
(2) X=Y=Z
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[#permalink]  11 Sep 2006, 09:38
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 suff-all 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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[#permalink]  11 Sep 2006, 09:48
(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]  11 Sep 2006, 09:50
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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[#permalink]  11 Sep 2006, 09:56
Hallo Fig,
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[#permalink]  11 Sep 2006, 10:03
I confirm

X^0=1 where X could be any real number
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[#permalink]  11 Sep 2006, 13:04
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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[#permalink]  11 Sep 2006, 13:21

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,

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[#permalink]  11 Sep 2006, 18:54
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
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[#permalink]  11 Sep 2006, 19:07
Same dilemma as everyone else. Vote for E
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[#permalink]  11 Sep 2006, 20:20
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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[#permalink]  11 Sep 2006, 21:44
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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[#permalink]  12 Sep 2006, 00:41
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, 02:10, edited 3 times in total.
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[#permalink]  12 Sep 2006, 00:48
C is right. 0^0 is invalid math expression. they can only be 1.
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[#permalink]  12 Sep 2006, 05:54
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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[#permalink]  12 Sep 2006, 06:11
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 easy-to-access 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.univ-nantes.fr/physique/perso/blanquet/conducti/a1besleg/a1besleg.htm

U can notice that k starts at 0 in
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[#permalink]  12 Sep 2006, 09:21
great discussion but whats the OA?
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[#permalink]  12 Sep 2006, 09:42
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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[#permalink]  12 Sep 2006, 09:50
Could we have the source of it?

PS: Those who want to try online 0^0
http://www.math.com/students/calculators/source/scientific.htm

PS2: A nice function drawer
http://www.coolmath.com/graphit/index.html
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[#permalink]  12 Sep 2006, 10:30
Fig wrote:
Could we have the source of it?

PS: Those who want to try online 0^0
http://www.math.com/students/calculators/source/scientific.htm

PS2: A nice function drawer
http://www.coolmath.com/graphit/index.html

Fig,

Don't rely on calculators but rely on math theorems.
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[#permalink] 12 Sep 2006, 10:30

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# The three integers X, Y, and Z. Is their product XYZ = zero

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