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:

Two numbers when divided by a divisor leave reminders of 248 [#permalink]

Show Tags

23 Nov 2011, 09:14

2

This post received KUDOS

13

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

74% (02:45) correct
26% (02:10) wrong based on 388 sessions

HideShow timer Statistics

Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.

Say the two numbers are x and y, and divisor is a.

x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.

x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.

From definitions above:

x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.

a*(N+K) + 620 = a*M + 68 552 = a*(M-N-K)

We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.

Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor. A) 276 B) 552 C) 414 D 1104 E) 2202

Thanks kostyan5. My approach is similar to that of urs. This is how i did it. Let the 2 numbers be X and Y; Let D= Divisor X = D*N+248 , N = Quotient got when X is divided by divisor R Y = D*K+372 , K = Quotient got when Y is divided by divisor R

X+Y = (D*N+248) + (D*K+372) = D(N+K)+620 = D(N+K+552/D)+68 As N+K+552/D must be an integer, D must be a factor of 552. As any divisor is greater than the reminder, D>372 So D=552 Answe B _________________

If u think this post is useful plz feed me with a kudo

Say the two numbers are x and y, and divisor is a.

x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.

x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.

From definitions above:

x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.

a*(N+K) + 620 = a*M + 68 552 = a*(M-N-K)

We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.

Therefore, a = 552. B.

ok, "a" must be at least 373, but then why not 414 instead of 552? Thanks!

If we follow kostyan5's way we get 552=a*(M-N-K) --> (M-N-K)=integer=552/a, no other value from the answer choices will yield an integer for this expression except 552 and 276, and as a>372 then a=552.

Re: Two numbers when divided by a divisor leave reminders of 248 [#permalink]

Show Tags

17 Dec 2013, 15:33

1

This post received KUDOS

cleetus wrote:

Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.

A. 276 B. 552 C. 414 D. 1104 E. 2202

Easy, why 68 if the sum of the remainders is 248+372=620? Cause the divisor is eating the other part. Then the divisor is 620-68=552

Say the two numbers are x and y, and divisor is a.

x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.

x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.

From definitions above:

x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.

a*(N+K) + 620 = a*M + 68 552 = a*(M-N-K)

We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.

Therefore, a = 552. B.

ok, "a" must be at least 373, but then why not 414 instead of 552? Thanks!

Say the two numbers are x and y, and divisor is a.

x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.

x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.

From definitions above:

x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.

a*(N+K) + 620 = a*M + 68 552 = a*(M-N-K)

We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.

Therefore, a = 552. B.

Why did you decide the a must be at least 373 and not 248? That's the other remainder.

Say the two numbers are x and y, and divisor is a.

x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division. y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.

x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.

From definitions above:

x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.

a*(N+K) + 620 = a*M + 68 552 = a*(M-N-K)

We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.

Therefore, a = 552. B.

Why did you decide the a must be at least 373 and not 248? That's the other remainder.

Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

So, the divisor mus be greater than both remainders, which means that a>372.

Re: Two numbers when divided by a divisor leave reminders of 248 [#permalink]

Show Tags

14 Nov 2013, 02:30

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: Two numbers when divided by a divisor leave reminders of 248 [#permalink]

Show Tags

01 May 2014, 03:05

jlgdr wrote:

cleetus wrote:

Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.

A. 276 B. 552 C. 414 D. 1104 E. 2202

Easy, why 68 if the sum of the remainders is 248+372=620? Cause the divisor is eating the other part. Then the divisor is 620-68=552

Answer is A Cheers! J

you mean B !!. Answer given is correct but option marked is incorrect. This was the smartest approach of the lot and I used the same..

If 620 is equating to 68 , what was the remaining amount ( 620 - 68). This added one unit to divisor

Re: Two numbers when divided by a divisor leave reminders of 248 [#permalink]

Show Tags

22 Jun 2015, 12:06

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...