kevincan wrote:

dahcrap wrote:

If a and b are positive integers such that a-b and a/b are both even integers, which of the following must be an odd integer?

A. a/2

B. b/2

C. (a+b) / 2

D. (2+a)/2

E. (2+b)/2

a and b must be even, and a must be a multiple of 4. D must be odd, as a + 2 is not a multiple of 4

i just finieshed manhattan's number properties and I am surprised they didn't cover a problem like this... they just said there "are no garuntees" when it comes to number properties and division by odds/evens. That's not true... if an odd number is divisble by an odd number, the result will always be odd.

so I got this question correct; but i plugged in numbers for C. (i used 0 and 2) but can you explain why a must be a multiple of four? (other than the fact that obviously it works)

like was there something that just clicked in your head when you looked at the question? i am generally intriqued by some of the folks on these boards and how they derive their answers.