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:

If x, a, and b are positive integers such that when x is [#permalink]

Show Tags

29 Sep 2010, 22:27

3

This post received KUDOS

40

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

50% (03:10) correct
50% (02:22) wrong based on 571 sessions

HideShow timer Statistics

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

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 \(b=a-1\)).

Thanks Bunnel!! Do you suggest using a particular strategy for these problems or using different strategy for every problem and whichever fits the bill for the given question..?

What do you mean by "these problems"? Remainder problems or must be true problems?

Re: If x, a, and b are positive integers such that when x is div [#permalink]

Show Tags

04 Sep 2012, 01:14

2

This post received KUDOS

sanjoo wrote:

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 divided by A, remainder is B, this implies A > B When divided by B, remainder is A-2, this implies B > A -2

Combining both, B < A < (B + 2) Since, A and B are integers, A = B + 1

Answer is (D) . Cheers! _________________

----------------------------------------------------------------------------------------- What you do TODAY is important because you're exchanging a day of your life for it! -----------------------------------------------------------------------------------------

Re: If x, a, and b are positive integers such that when x is [#permalink]

Show Tags

03 Nov 2013, 01:50

2

This post received KUDOS

This problem can be solved by plugging numbers. For instance if x=5, a=3, b=2 we get: ...when x is divided by a, the remainder is b... > 5/3=1+2/3 ...and when x is divided by b, the remainder is a-2... > 5/2=2+1/2

Both work. If we plug numbers into the answers, only D will work.

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.

Hi Bunuel,

I solved this problem with a bit different approach x = p*a + b..........eqn(1) and x = q*b + (a-2)..............eqn(2)

now, equating eqn(1) and eqn(2) p*a + b = q*b + (a-2)

a(p-1) = b(q-1) - 2 if we put p = q = 3

we get, 2a = 2b - 2 or a = b - 1 or a + 2 = b + 1 which is option E

would pl tell me where am i wrong with my approach?? Thanks.

You cannot assign arbitrary values to p and q and say that p = q = 3. _________________

Re: If x, a, and b are positive integers such that when x is [#permalink]

Show Tags

21 Oct 2014, 18:26

1

This post received KUDOS

So the thing to keep in mind with remainder problems like this is that it usually involves finding a value from knowing that the remainder must be smaller than the quotient. From this, we know that a>b and that b>a-2, put these two together and we get: a>b>a-2 and since these are all positive integers then there b must equal a-2 _________________

Re: If x, a, and b are positive integers such that when x is [#permalink]

Show Tags

13 Nov 2014, 15:20

1

This post received KUDOS

Since we know that the remainder is b when x is divided by a we know that b is smaller than a. We also know that a-2 is smaller than b, because a-2 is the remainder when x is divided by b. If we put those two together we know that: a-2<b<a

Because we know that x, a and b are all positive integers we also know that b must be a-1, because it is an integer that is bigger than a-2 and smaller than a _________________

Thanks Bunnel!! Do you suggest using a particular strategy for these problems or using different strategy for every problem and whichever fits the bill for the given question..?

Thanks Bunnel!! Do you suggest using a particular strategy for these problems or using different strategy for every problem and whichever fits the bill for the given question..?

What do you mean by "these problems"? Remainder problems or must be true problems?

Bunnel, thanks so much for the compilation! By 'these problems' I meant 'Must be true' questions in which at times you have more than 1 correct answers. My apologies for the lack of clarity their. Your compilation should be enough to practice. Thanks again!

Re: If x, a, and b are positive integers such that when x is [#permalink]

Show Tags

05 Sep 2012, 23:56

Bunuel wrote:

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.

Indeed very nice explanation, but for me, for the person who is not that strong in quants sometimes difficult to keep all that concepts in my head and i am jumping to different approaches. Whenever i see must be true questions i plug in some numbers and see which answer works, since it is must be true questions any numbers should work equally. For example in this problem: lets says x=5, a=3 then b=2, so check all the answers and we see that only d works, but if there will be two answers that work try different numbers till we get only one. It could be time consuming, but when we are asked simple expressions it is easy to find numbers that work well.

Bunuel, do you think there are any pitfalls that i should be aware of? _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: If x, a, and b are positive integers such that when x is [#permalink]

Show Tags

20 Apr 2013, 12:57

My approach of plug in numbers was certainly not the best approach, in a zest of GMAT I dont know why I am loosing to think simple....this was a simple algebra which I complicated with numbers _________________

"When the going gets tough, the tough gets going!"

Check out this awesome article about Anderson on Poets Quants, http://poetsandquants.com/2015/01/02/uclas-anderson-school-morphs-into-a-friendly-tech-hub/ . Anderson is a great place! Sorry for the lack of updates recently. I...

As you leave central, bustling Tokyo and head Southwest the scenery gradually changes from urban to farmland. You go through a tunnel and on the other side all semblance...

Ghibli studio’s Princess Mononoke was my first exposure to Japan. I saw it at a sleepover with a neighborhood friend after playing some video games and I was...