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very good one [#permalink]

14 Jun 2010, 15:00

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I dont usually post on Quant Forum, but I consider this an interesting one:

X, A, and B are positive integers. When X is divided by A , the remainder is B . If when X is divided by B , the remainder is A-2 , which of the following must be true?

a)A is even
b)X+B is divisible by A
c)X-1 is divisible by A
d)B=A-1
e)A+2=B+1
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Last edited by noboru on 14 Jun 2010, 15:50, edited 1 time in total.

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Re: very good one [#permalink]

14 Jun 2010, 15:14

noboru wrote:

When X is divided by A , the remainder is B
=> A>B as the remainder is always left when it is less than the divisor else it is divided again.

when X is divided by B , the remainder is A-2
=> B > A-2 , same explanation.

combine both..... A>B>A-2 => A+2 > B+2 > A

This is only possible when B+1 = A as they are integers.
Take eg of A = 5, B= 4 and A-2 = 3

But this option is not listed , I guess there is a typo error in d or e as they both are equal.
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Re: very good one [#permalink]

14 Jun 2010, 15:36

noboru wrote:

When X is divided by A, the remainder is B --> x=aq+b --> remainder=b<a=divisor (remainder must be less than divisor);
When X is divided by B, the remainder is A-2 --> x=bp+(a-2) --> remainder=(a-2)<b=divisor.

So we have that: a-2<b<a, as a and b are integers, then it must be true that b=a-1 (there is only one integer between a-2 and a, which is a-1 and we are told that this integer is b, hence b=a-1).

No one seems to be necessarily true from answer choices. One thing though D and E are the same, so there must be a typo: if D were b=a-1, instead of b=a+1, then D would be the correct answer OR if E were a-2=b-1, instead of a+2=b+1, then E would be the correct answer.

Pleas check the answer choices.
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Re: very good one [#permalink] 14 Jun 2010, 15:36

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very good one

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