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# If Z is a positive integer, x*z=0? 1) x*z=-3x 2) x*z=3x

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Senior Manager
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If Z is a positive integer, x*z=0? 1) x*z=-3x 2) x*z=3x [#permalink]  11 May 2005, 19:37
If Z is a positive integer, x*z=0?
1) x*z=-3x
2) x*z=3x
VP
Joined: 13 Jun 2004
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a good one, i am not so sure

in statement 1 we know that Z is a positive integer so there is no way Z=-3, the only solution is that Z is equal to any positive number but that X=0 so XZ=0 -> suff

in statement 2, Z could be for example 3 and X could also be 3. Not suff
VP
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Antmavel wrote:
a good one, i am not so sure, I would answer A
in statement 1 we know that Z is a positive integer so there is no way Z=-3, the only solution is that Z is equal to any positive number but that X=0 so XZ=0 -> suff. in statement 2, Z could be for example 3 and X could also be 3. Not suff

If Z is a positive integer, x*z=0?
1) x*z=-3x
2) x*z=3x

Answer should be A, but this is one of the poorly worded question because it is not possible to have x*z=-3x = 3x without combining i and ii. to satisfy booth statement x must be o and ETS doesnot ask such question. only after combining both, we know that x = o. therefore no wonder if OA is C.
CIO
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MA wrote:
Antmavel wrote:
a good one, i am not so sure, I would answer A
in statement 1 we know that Z is a positive integer so there is no way Z=-3, the only solution is that Z is equal to any positive number but that X=0 so XZ=0 -> suff. in statement 2, Z could be for example 3 and X could also be 3. Not suff

If Z is a positive integer, x*z=0?
1) x*z=-3x
2) x*z=3x

Answer should be A, but this is one of the poorly worded question because it is not possible to have x*z=-3x = 3x without combining i and ii. to satisfy booth statement x must be o and ETS doesnot ask such question. only after combining both, we know that x = o. therefore no wonder if OA is C.

I'm not so sure it's a bad question. Certainly it's confusing. But if * is a special function, then we don't know anything about the relationship of x and z. Maybe from one we could learn that * means "lose z and multiply by negative 3".

Either way, with C we see that 3x = -3x, and only zero could make that work.
VP
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"A"

I don't see any ambiguity in this ques, perhaps I am missing something

state 1....x*z + 3x = 0

x(z+3) = 0........so solutions are x = 0 or z = -3 or x = 0 and
z = -3..but Z > 0....so only X can be 0.....so X*Z = 0

state 2....x*z - 3x = 0

x(z-3) = 0......X = 0 or Z= 3 or X=0 and Z = 3.....insuff
VP
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banerjeea_98 wrote:
"A". I don't see any ambiguity in this ques, perhaps I am missing something

in isolation, that is ok. but if you see the question in totality, seems something wired.
GMAT Club Legend
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If z is positive, the only way x*z can be 0 is for x to be 0. So the question is really asking Is x 0?

(1) x*z = -3x --> tells us x = -x since z is positive. So x must be 0. Sufficient.
(2) z=3. Doesn't really tells us anything. x can be 0 and x*z = 3x. Or x can be any value and still satisfy statement 2.

Ans: A
Senior Manager
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ywilfred wrote:
If z is positive, the only way x*z can be 0 is for x to be 0. So the question is really asking Is x 0?

(1) x*z = -3x --> tells us x = -x since z is positive. So x must be 0. Sufficient.
(2) z=3. Doesn't really tells us anything. x can be 0 and x*z = 3x. Or x can be any value and still satisfy statement 2.

Ans: A

Agreed... good explanation
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