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# very good one

Author Message
VP
Joined: 16 Jul 2009
Posts: 1487

Kudos [?]: 1456 [0], given: 2

Schools: CBS
WE 1: 4 years (Consulting)

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14 Jun 2010, 15:00
00:00

Difficulty:

(N/A)

Question Stats:

50% (02:51) correct 50% (00:00) wrong based on 3 sessions

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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.

Kudos [?]: 1456 [0], given: 2

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2761

Kudos [?]: 1887 [0], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35

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14 Jun 2010, 15:14
noboru wrote:
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

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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Kudos [?]: 1887 [0], given: 235

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 129248 [0], given: 12196

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14 Jun 2010, 15:36
noboru wrote:
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

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.

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Kudos [?]: 129248 [0], given: 12196

Re: very good one   [#permalink] 14 Jun 2010, 15:36
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