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If a and b are positive integers such that a-b and a/b are

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If a and b are positive integers such that a-b and a/b are [#permalink] New post 26 Jul 2007, 13:38
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
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 [#permalink] New post 26 Jul 2007, 14:17
C, but it only works for some of the numbers I can think of.

60, 10 works, 70, 10 doesn't.
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Re: Need some help here [#permalink] New post 26 Jul 2007, 14:31
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
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Re: Need some help here [#permalink] New post 26 Jul 2007, 14:44
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


Ah I missed the multiple of 4 thing. Thanks Kevin
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 [#permalink] New post 26 Jul 2007, 17:20
a-b = even -> both a and b even, or both a and b odd.
a/b = even -> could be 4/2, 8/2, 8/4, 16/4...etc...

A,B -> A and B could be 4, 8...etc
C -> A and B could be 8 and 4, then a+b/2 = even. Out.
D -> In. a is a multiple of 4, so 2+a/2 = odd.
E -> b could be 2, then 2+b/2 = even. Out.

Ans D
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Re: Need some help here [#permalink] New post 26 Jul 2007, 17:38
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.
Re: Need some help here   [#permalink] 26 Jul 2007, 17:38
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