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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]

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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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Senior Manager
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24 Jun 2006, 17:17
1
KUDOS
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: 02 Mar 2006
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Location: France

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24 Jun 2006, 16:32
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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24 Jun 2006, 17:16
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 ?

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Director
Joined: 16 Aug 2005
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24 Jun 2006, 18:20
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!

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Senior Manager
Joined: 16 Apr 2006
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24 Jun 2006, 21:46
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

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Intern
Joined: 22 Jun 2006
Posts: 49

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Location: Big Apple

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24 Jun 2006, 23:46
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.

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Director
Joined: 02 Mar 2006
Posts: 577

Kudos [?]: 130 [0], given: 0

Location: France

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25 Jun 2006, 01:10
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.

Kudos [?]: 130 [0], given: 0

25 Jun 2006, 01:10
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