Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

\(X\) , \(A\) , 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 ...

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

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)

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.

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 _________________

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.

\(X\) , \(A\) , 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 \(b=a-1\)).

\(X\) , \(A\) , 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?)