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The three integers X, Y, and Z. Is their product XYZ = zero [#permalink ]
26 Jun 2003, 03:07

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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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(1): X^Y=1 alone is sufficient to tell us that Y is 0 and therefore X*Y*Z=0

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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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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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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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btw, this DS question is from which source ?

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Thanks,

What would you have said "C' or "E"?

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Now... what's the OA?

C / E

Personally, I'll go with C

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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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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/np-exponents.cfm ), thus you won't see such question on the real test.

Hope it helps.

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