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Director
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X,A,B are positive integers. When X is divided by A, the [#permalink]
 24 Jun 2006, 15:21
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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
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Director
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That's nice. OA D. I could'nt find out how to pick numbers for this problem.
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Senior Manager
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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 ?
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Senior Manager
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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)
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Director
Joined: 16 Aug 2005
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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!
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Senior Manager
Joined: 16 Apr 2006
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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
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Intern
Joined: 22 Jun 2006
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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. 
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Director
Joined: 02 Mar 2006
Posts: 582
Location: France
Followers: 1
Kudos [?]:
2
[0], given: 0
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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. 
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