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# X ,A , and B are positive integers. When X is divided by A,

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VP
Joined: 22 Nov 2007
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X ,A , and B are positive integers. When X is divided by A, [#permalink]  02 Mar 2008, 03:27
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X ,A , and B are positive integers. When X is divided by A, the remainder is B. When X is divided by B, the remainder is A-2 . Which of the following must be true?
 A is even
 X+B is divisible by A
 X-1 is divisible by A
 B=A-1
 A+2=B+1
Senior Manager
Joined: 20 Dec 2004
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Re: Remainder and integers [#permalink]  02 Mar 2008, 05:53
Is it D..? Not sure but this is what I would have picked in the real exam

X=An + B
X = Bm + (A - 2)

An + B = Bm + (A - 2)

B (m - 1) = A (n - 1) + 2

try substituting...basically "some multiple of B" equals "some multiple of A" + 2

2 ( 4 ) = 3 (2) + 2....

Hence D...
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VP
Joined: 22 Nov 2007
Posts: 1104
Followers: 8

Kudos [?]: 215 [0], given: 0

Re: Remainder and integers [#permalink]  03 Mar 2008, 09:48
I actually can't follow this step:

B (m - 1) = A (n - 1) + 2

try substituting...basically "some multiple of B" equals "some multiple of A" + 2

2 ( 4 ) = 3 (2) + 2....

anyway I saw this alternative explanation:

since any remainder must be smaller than its divisor, B<A and A-2<B. the only choice which follows this condition is D
Re: Remainder and integers   [#permalink] 03 Mar 2008, 09:48
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