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

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stolyar
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The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   26 Jun 2003, 04:07
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The three integers X, Y, and Z. Is their product XYZ = zero

(1) X^Y=1
(2) X=Y=Z

:shh

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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   26 Jun 2003, 04:26
(1): X^Y=1 alone is sufficient to tell us that Y is 0 and therefore X*Y*Z=0
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   26 Jun 2003, 04:59
You're right Stolyar - I didn't think of that.

Then neither statements are sufficient
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   26 Jun 2003, 06:58
is it C.

from 1: x^y=1 only in 2 cases 0^1 and 1^1 in both cases y=1.

from 2: u cant say anyting

both: x=y=z=1, then xyz=1. so no is the answer
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   26 Jun 2003, 22:22
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arun wrote:
is it C.

from 1: x^y=1 only in 2 cases 0^1 and 1^1 in both cases y=1.

from 2: u cant say anyting

both: x=y=z=1, then xyz=1. so no is the answer


lots of mistakes; even so, C is correct

(1) X^Y=1 follows that 1^1=1, 0^1=1, and –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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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   08 Jul 2003, 19:19
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stolyar wrote:
arun wrote:
is it C.

from 1: x^y=1 only in 2 cases 0^1 and 1^1 in both cases y=1.

from 2: u cant say anyting

both: x=y=z=1, then xyz=1. so no is the answer


lots of mistakes; even so, C is correct

(1) X^Y=1 follows that 1^1=1, 0^1=1, and тАУ1^0=1: NOT ENOUGH
(2) is of no use

combine X=Y=Z=1, so the product does not equal to a zero.

thus, C.



Fabulous problem !!!!!!


0^1 = 0 just like 5^1=5 :wink:
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   31 May 2010, 11:18
From statement 1, 0^0= 1 so X=y=z is also sufficient when all are 0.
so the answer must be E.
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   31 May 2010, 11:26
The three integers X, Y, and Z. Is their product XYZ = zero

(1) X^Y=1
(2) X=Y=Z


CAN ANYONE HELP ME?
I think it is E.
As combining both statement we have two possible values for x=y=z.
Combining statement 1 and 2, there could be two values (x,y,z)= (1,1,1) or (0,0,0)
But where i am confused is that - can we say 0^0=1 for statement 1. If we can't, then the answer must be C not E.
Let me know what GMAT says about 0^0.
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   31 May 2010, 12:00
The value of any number raised to 0 is 1, though the opinion regarding the value of 0^0 differs across various sources :)



check this : 0-raised-to-90605.html
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   31 May 2010, 12:06
btw, this DS question is from which source ?
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   31 May 2010, 12:07
Thanks,
What would you have said "C' or "E"?
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   02 Jun 2010, 10:34
Now... what's the OA?

C / E

Personally, I'll go with C
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   02 Jun 2010, 11:40
The three integers X, Y, and Z. Is their product XYZ = zero

(1) X^Y=1
(2) X=Y=Z

st 1.
it tells us that X=1 but Y could be 0 or any positive integer besides 0. INSUFF
st 2.
INSUFF

st1+st2
they tell us that a X=Y=Z=1. SUFF to prove that XYZ does not equal 0.
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   02 Jun 2010, 12:17
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The three integers X, Y, and Z. Is their product XYZ = zero

(1) X^Y=1
(2) X=Y=Z

This is not a good question because to answer it we should answer to the question \(0^0=?\)

0^0, in some sources equals to 1, some mathematicians say it's undefined.

If we say that \(0^0=undefined\), then the answer would be C.

If we say that \(0^0=1\), then the answer would be E.

BUT: the case of 0^0 is not tested on the GMAT (https://www.manhattangmat.com/np-exponents.cfm), thus you won't see such question on the real test.

Hope it helps.
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   03 Jun 2010, 13:43
Thanks to All of you!
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink] New post   24 Dec 2021, 03:24
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Re: The three integers X, Y, and Z. Is their product XYZ = zero [#permalink]
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