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

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Director
Joined: 02 Mar 2006
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X,A,B are positive integers. When X is divided by A, the [#permalink]  24 Jun 2006, 14:21
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X,A,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 if the following must be true?

1. A is even
2. X+B is divisible by A
3. X-1 is divisible by A
4. B=A-1
5. A+2=B+1
Director
Joined: 02 Mar 2006
Posts: 579
Location: France
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Kudos [?]: 47 [0], given: 0

[#permalink]  24 Jun 2006, 15:32
That's nice. OA D. I could'nt find out how to pick numbers for this problem.
Senior Manager
Joined: 12 Mar 2006
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Schools: Kellogg School of Management
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[#permalink]  24 Jun 2006, 16:16
X & Y wrote:
D

Try this values:

X=7
A=2
B=1

X=17
A=3
B=2

Hi X&Y

I understand that these numbers work for the case mentioned above but i am not able to get a proof that can say that B must be equal to A-1.

I have the equations X = nA + B and X = pB + A-2 where n and p are integers, but dont know how to proceed. Could you please explain ?
Senior Manager
Joined: 07 Jul 2005
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Location: Sunnyvale, CA
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[#permalink]  24 Jun 2006, 16:17
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When divided by A, remainder is B, this implies
A > B

Similarly,
B > A -2

Combining,
B < A < (B + 2)
Since, A and B are integers,
A = B + 1

(D)
Director
Joined: 16 Aug 2005
Posts: 946
Location: France
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[#permalink]  24 Jun 2006, 17:20
sgrover wrote:
When divided by A, remainder is B, this implies
A > B

Similarly,
B > A -2

Combining,
B < A < (B + 2)
Since, A and B are integers,
A = B + 1

(D)

_________________

I believe its yogurt!

Senior Manager
Joined: 16 Apr 2006
Posts: 280
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[#permalink]  24 Jun 2006, 20:46
Quote:
When divided by A, remainder is B, this implies
A > B

Similarly,
B > A -2

Combining,
B < A < (B + 2)
Since, A and B are integers,
A = B + 1

(D)

That's Great
Intern
Joined: 22 Jun 2006
Posts: 49
Location: Big Apple
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Kudos [?]: 0 [0], given: 0

[#permalink]  24 Jun 2006, 22:46
sgrover wrote:
When divided by A, remainder is B, this implies
A > B

Similarly,
B > A -2

Combining,
B < A < (B + 2)
Since, A and B are integers,
A = B + 1

(D)

GREAT explanation. Thanks.
Director
Joined: 02 Mar 2006
Posts: 579
Location: France
Followers: 1

Kudos [?]: 47 [0], given: 0

[#permalink]  25 Jun 2006, 00:10
sgrover wrote:
When divided by A, remainder is B, this implies
A > B

Similarly,
B > A -2

Combining,
B < A < (B + 2)
Since, A and B are integers,
A = B + 1

(D)

Thanks, you got it.
[#permalink] 25 Jun 2006, 00:10
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# X,A,B are positive integers. When X is divided by A, the

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