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M16 Q35 PS from GMAT club tests [#permalink]
14 Aug 2008, 08:25

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Difficulty:

55% (hard)

Question Stats:

47% (02:26) correct
53% (01:33) wrong based on 256 sessions

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

Re: PS from GMAT club test M16 Q35 [#permalink]
14 Aug 2008, 08:42

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durgesh79 wrote:

spent 10 minutes on this one .... and finally guessed it and it was right ...

X, A, and 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 of the following must be true?

A is even X+B is divisible by A X-1 is divisible by A B = A-1 A+2 = B+1

Re: PS from GMAT club test M16 Q35 [#permalink]
14 Aug 2008, 08:58

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durgesh79 wrote:

spent 10 minutes on this one .... and finally guessed it and it was right ...

X, A, and 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 of the following must be true?

A is even X+B is divisible by A X-1 is divisible by A B = A-1 A+2 = B+1

D firm:

When X is divided by A, the remainder is B. -- means A>B (remainder always less A)

Re: M16 Q35 PS from GMAT club tests [#permalink]
27 Apr 2010, 22:07

Also from substitution method it we can see that by taking numbers for A and B , taking 3 and 2 the closer number would be 5, as the conditions get satisfied so we can assure that 3 and 2 are A,B. Thus satisfies the conditions.

Re: M16 Q35 PS from GMAT club tests [#permalink]
28 Apr 2011, 09:20

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spent more than 10 min trying to solve, finally substituted numbers (A=3, B=2) to arrive at (D) ... great approach by x2suresh ... divisor>remainder ... life can be so simple _________________

Re: M16 Q35 PS from GMAT club tests [#permalink]
02 May 2012, 10:29

Excellent Concept Problem: D is correct answer.

When X is divided by A, the remainder is B. => A > B When X is divided by B, the remainder is (A-2). => B > A - 2 Combining the two inequalities: A > B > A - 2 i.e.: B is between A and (A-2), so B must be equal to A-1. B = A - 1. (D) is the correct answer.

Re: M16 Q35 PS from GMAT club tests [#permalink]
03 May 2013, 04:18

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Expert's post

durgesh79 wrote:

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

spent 10 minutes on this one .... and finally guessed it and it was right ...

BELOW IS REVISED VERSION OF THIS QUESTION:

If x, a, and b are positive integers such that when x is divided by a, the remainder is b and when x is divided by b, the remainder is a-2, then 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).

Re: M16 Q35 PS from GMAT club tests [#permalink]
18 Apr 2014, 05:50

Bunuel wrote:

durgesh79 wrote:

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

spent 10 minutes on this one .... and finally guessed it and it was right ...

BELOW IS REVISED VERSION OF THIS QUESTION:

If x, a, and b are positive integers such that when x is divided by a, the remainder is b and when x is divided by b, the remainder is a-2, then 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).

Answer: D.

Do you have any suggestions on how one can be quick at finding this insight? (And finding the correct insight quickly in general?)