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



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DS: POWERS [#permalink]
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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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DS: POWERS [#permalink]
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26 Jun 2003, 04:59
You're right Stolyar  I didn't think of that.
Then neither statements are sufficient



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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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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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Is 0^1 = 1 ???



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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



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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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Am i right? [#permalink]
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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: Am i right? [#permalink]
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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 : 0raisedto90605.html
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Re: Am i right? [#permalink]
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31 May 2010, 12:06
btw, this DS question is from which source ?
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Re: Am i right? [#permalink]
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31 May 2010, 12:07
Thanks, What would you have said "C' or "E"?
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Re: DS: POWERS [#permalink]
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02 Jun 2010, 10:34
Now... what's the OA? C / E Personally, I'll go with C
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Re: DS: POWERS [#permalink]
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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: DS: POWERS [#permalink]
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02 Jun 2010, 12:17
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 ( http://www.manhattangmat.com/npexponents.cfm), thus you won't see such question on the real test. Hope it helps.
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Re: DS: POWERS [#permalink]
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03 Jun 2010, 13:43
Thanks to All of you!
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