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:

When S is divided by 5 remainder is 3, when it is divided by 7, remainder is 4. If K+S is divisible by 35, what is the least possible value of K?

Or by Chinese modulus theorem, we have, from what is provided,
S=35n +18 ( n is integer)
S+ K= 35n +18+ K, 35n is divisible by 35 ---> the least possible value of K= 17 so that S+ K= 35n + 35

When S is divided by 5 remainder is 3, when it is divided by 7, remainder is 4. If K+S is divisible by 35, what is the least possible value of K?

Or by Chinese modulus theorem, we have, from what is provided, S=35n +18 ( n is integer) S+ K= 35n +18+ K, 35n is divisible by 35 ---> the least possible value of K= 17 so that S+ K= 35n + 35

When S is divided by 5 remainder is 3, when it is divided by 7, remainder is 4. If K+S is divisible by 35, what is the least possible value of K?

Or by Chinese modulus theorem, we have, from what is provided, S=35n +18 ( n is integer) S+ K= 35n +18+ K, 35n is divisible by 35 ---> the least possible value of K= 17 so that S+ K= 35n + 35

Pls explain how you got the below stmt

S=35n +18 ( n is integer)

We have:
S= 3(mod 5) or S= 4(mod 7)
S= 5m+ 3 ( m is integer) --> 5m+3= 4 ( mod 7) --> 5m= 1(mod 7) --> m= 3 ( mod 7 ) (the method is to try different remainders of 7, starting from 1) --> m= 7n + 3 ( n is integer) --> substitute m by n, we have:
S= 35n+ 18

The above method is so-called Chinese modulus theorem . I saw some above post have the link to this theorem.

When S is divided by 5 remainder is 3, when it is divided by 7, remainder is 4. If K+S is divisible by 35, what is the least possible value of K?

Or by Chinese modulus theorem, we have, from what is provided, S=35n +18 ( n is integer) S+ K= 35n +18+ K, 35n is divisible by 35 ---> the least possible value of K= 17 so that S+ K= 35n + 35

Pls explain how you got the below stmt

S=35n +18 ( n is integer)

We have: S= 3(mod 5) or S= 4(mod 7) S= 5m+ 3 ( m is integer) --> 5m+3= 4 ( mod 7) --> 5m= 1(mod 7) --> m= 3 ( mod 7 ) (the method is to try different remainders of 7, starting from 1) --> m= 7n + 3 ( n is integer) --> substitute m by n, we have: S= 35n+ 18

The above method is so-called Chinese modulus theorem . I saw some above post have the link to this theorem.

I like to add that the CRT works only if the mod values are relatively prime.

For three facts relating to S, I think it can be worked out but would require a very exhaustive method that invovles euclidean algorithm...

Here's a link, that shows how to solve for 3 facts using the CRT.