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# If A and B are positive integers such that A-B and A/B are

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Senior Manager
Joined: 22 Sep 2005
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Kudos [?]: 89 [0], given: 1

If A and B are positive integers such that A-B and A/B are [#permalink]  25 Jan 2008, 10:03
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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) (A+2)/2
E) (B+2)/2
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2143 [0], given: 359

Re: PS: Odd or even [#permalink]  25 Jan 2008, 12:29
Expert's post
D

A-B and A/B are both even integers.

from A/B - (A-even and B - odd) or (A=2^n*even, B - even)
from A-B - (A-even and B - even) or (A - odd, B - odd)

only (A=2^n*even, B - even) - (A=2^k*X, B=2^m*Y; m>0, k>m)

(A+2)/2= A/2+1=even+odd=odd
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Joined: 28 Dec 2005
Posts: 1583
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Kudos [?]: 88 [0], given: 2

Re: PS: Odd or even [#permalink]  25 Jan 2008, 12:53
walker wrote:
D

A-B and A/B are both even integers.

from A/B - (A-even and B - odd) or (A=2^n*even, B - even)
from A-B - (A-even and B - even) or (A - odd, B - odd)

only (A=2^n*even, B - even) - (A=2^k*X, B=2^m*Y; m>0, k>m)

(A+2)/2= A/2+1=even+odd=odd

walker, i had the same approach as you , except i didnt break up the expression into A/2 + 1, and this was the logic:

(A+2)/2 = (even + even) / even = even

Why doesnt that work ?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2143 [0], given: 359

Re: PS: Odd or even [#permalink]  25 Jan 2008, 13:01
Expert's post
pmenon wrote:
(A+2)/2 = (even + even) / even = even

Why doesnt that work ?

(2+2)/2=2
(4+2)/2=3

even/even is odd (if numerator is not divisible by 4) or even (if numerator is divisible by 4)
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Re: PS: Odd or even   [#permalink] 25 Jan 2008, 13:01
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