Statements NEVER contradict each other in DS !

[MdAbuAsad]

Source: Self-made (Modified question)

if x and p are positive integers, is xp divisible by 3?
(1) x=69
(2) x=96

Hi Ron, i got a hint from Manhattan GMAT books about the fact that "the two statements NEVER contradict each other''. If i try to make the solution, then i got the correct answer D. But, here the two statements totally contradict each other. So, my question is: is the question stem with two statements legitimate? . If it is not the legitimate question, could you explain details, please?
Thanks....

N.B.: Ron, i'm totally newcomer in Quant part- i've no knowledge in mathematics. So, if i make any mistake by modifying this question then i'm sorry.

[RonPurewal]

statement 1 and statement 2 won't contradict each other.
the point is that it will ALWAYS be POSSIBLE to combine the statements -- even if you don't have to.
obviously we can't combine the statements x = 69 and x = 96, so... yeah, this "problem" doesn't have an acceptable format.

[RonPurewal]

more importantly, though -- there's no reason for you to worry about this, since there's no way it can give you an actual advantage on the test.
all of the problems WILL have this format -- with 2 statements that are consistent with each other -- so, there's nothing here that you can use to actually help you eliminate, narrow, or solve anything.

(in other words, if there were WRONG things with contradictory statements, THEN, knowing this principle would actually let you eliminate those things. but, since you will never see anything that actually violates this principle, knowing it won't confer any advantage on you.)

[MdAbuAsad]

Thank you Ron for your cordial response.

obviously we can't combine the statements x = 69 and x = 96, so... yeah, this "problem" doesn't have an acceptable format


all of the problems WILL have this format -- with 2 statements that are consistent with each other-- so, there's nothing here that you can use to actually help you eliminate, narrow, or solve anything..

Ron, could you make clear to me by giving an example why '''we can't combine the statements x = 69 and x = 96''', please?

how two statements consistent with each other, can you give me an example to eradicate my confusion?
finally, does MY two statements contradict each other?

also,
though it is not my duty in the real exam to prove ''Statements NEVER contradict each other in DS', i've a curiosity to know the facts that HOW ''Statements NEVER contradict each other in DS''?

Thanks again..[/quote]

[tim]

Everything you are saying is so unclear, it's impossible to know what you will consider an acceptable answer to your question. For instance, you are asking for an "example" of why we can't have two contradictory statements on the GMAT. That's like asking for an "example" of why the sky is blue. There are no "examples", it just IS.

x cannot have two different values, so when you give two different values in your problem, you have created a contradiction just like I would if I said "I am 26 years old and I am also 55 years old". This can't happen on the GMAT, so your problem is not a real problem. It doesn't prove the GMAT wrong or anything; remember, THEY are the ones who made the rule that the statements won't contradict each other. That is why Ron said you shouldn't waste your time on a problem like this - it is nothing like a real GMAT problem.