Odd or Even Medium

[cschramke]

I understand all but one part of this CAT 2 exam Q:

If , abs(x - 9/2)=5/2, and if y is the median of a set of p consecutive integers, where p is odd, which of the following must be true?

I. xyp is odd

II. xy(p2 + p) is even

III. x2y2p2 is even

The answer states that if X is negative, i.e. X - 9/2 = - 5/2, then x = 2... but then it says X could be odd or even. How can it be odd or even when both possible X's are positive (7 and 2)?

[RonPurewal]

How can it be odd or even when both possible X's are positive (7 and 2)?

i'm sorry, i'm not understanding your question here.

it actually doesn't matter here whether x is positive or negative, because nothing in the problem depends on signs; everything in the problem deals exclusively with the distinction between odd and even.
so, the point is that 2 is even and 7 is odd. test each of those cases separately, and you'll find what you're looking for.

[NikhilS427]

But y can also be 0
Say the sequence is -2,-1,0,1,2
The median is 0. So none of these options 'MUST' be true. I believe this question should be modified or it could confuse many people.

[tim]

No, II is still true. What makes you think it isn't? Have you fallen for the trap of assuming (contrary to very definition of "even") that 0 is not an even number?

Remember, everyone:
0 is even (if that is not obvious, you need to review the definition of even)
0 is an integer (if that is not obvious, you need to review the definition of an integer)
0 is neither positive nor negative (if that is not obvious, you need to review the definition of positive and negative)
0 is a multiple of every integer (if that is not obvious, you need to review the definition of a multiple)

[RonPurewal]

more importantly, the official problems are, pretty much without exception, written so that these 'fringe' cases DO NOT AFFECT the outcome of the problem.

for example, 0 is even (as discussed here), and 1 is not a prime number.
but the chance that an official GMAC problem will actually DEPEND on these things is pretty much nil.
see, if that were to happen, then we'd essentially have a 'trick question'—the answer would depend not on skills that are actually important (like pattern recognition), but, rather, on weird nitpicky niceties of definitions.

don't forget, the writers do a very VERY good job of making this test free from 'trick questions'. so, if you're unsure about some 'weird' case, the answer should be the same as what you'd get by ignoring that case altogether.
...at least that's how the official test will work. (if you find one of our problems that doesn't work like this, please bring it to our attention!)