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 m is divided by 7, the remainder is 5. When m is divided by 13 [#permalink]

Show Tags

17 Aug 2016, 18:54

1

This post received KUDOS

4

This post was BOOKMARKED

first, find the lowest value of m: formula is m=r+dq, or m=remainder+divisor*quotient assume quotient of m/7=2 and quotient of m/13=1 thus, 5+7*2=19 and 6+13*1=19 then, find the next value of m: add the product of two divisors, or 7*13=91, to 19, for a sum of 110 m=110

Re: When m is divided by 7, the remainder is 5. When m is divided by 13 [#permalink]

Show Tags

17 Aug 2016, 20:44

gracie wrote:

first, find the lowest value of m: formula is m=r+dq, or m=remainder+divisor*quotient assume quotient of m/7=2 and quotient of m/13=1 thus, 5+7*2=19 and 6+13*1=19 then, find the next value of m: add the product of two divisors, or 7*13=91, to 19, for a sum of 110 m=110

Thanks gracie, I was trying to recollect this for awhile. It's called Chinese Remainder Theorem.

When m is divided by 7, the remainder is 5. When m is divided by 13 [#permalink]

Show Tags

17 Aug 2016, 21:26

4

This post was BOOKMARKED

Senthil1981 wrote:

gracie wrote:

first, find the lowest value of m: formula is m=r+dq, or m=remainder+divisor*quotient assume quotient of m/7=2 and quotient of m/13=1 thus, 5+7*2=19 and 6+13*1=19 then, find the next value of m: add the product of two divisors, or 7*13=91, to 19, for a sum of 110 m=110

Thanks gracie, I was trying to recollect this for awhile. It's called Chinese Remainder Theorem.

Hi Senthil, You're welcome. Here's something I forgot to mention: when you're trying to pick the quotients, remember that the ratio between them will inversely approximate the ratio between divisors. In the problem above, the ratio between divisors is 7:13, while the ratio between quotients is 2:1. I hope this is helpful. gracie

When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m?

A. 5 B. 19 C. 61 D. 74 E. 110

Use some logic to solve it orally.

Note here that the two divisors are 7 and 13. So when you get the first value of m that satisfies these conditions, you know that you will get all subsequent values by adding 7*13 = 91 to them progressively.

So, if 5 were a value of m, there would be other values of m such as 5+91, 5+91+91 etc.

Hence, all (A), (B), (C) and (D) cannot be the maximum values of m since when you add 91 to them, you will get a value of m less than 200 and that will be the maximum. Hence, answer has to be (E) only.

Re: When m is divided by 7, the remainder is 5. When m is divided by 13 [#permalink]

Show Tags

20 Aug 2016, 10:51

1

This post received KUDOS

1

This post was BOOKMARKED

Bunuel wrote:

When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m?

A. 5 B. 19 C. 61 D. 74 E. 110

Using Bunuel's formula -

m = 7x +5 : 12,19,26 .. m = 13y +6 : 19,...

For quotient, LCM (7,13) =91 For remainder, first common value of each pattern i.e. 19 so we can put m as -> m = 91q + 19 Now 1 < m < 200 putting q=2 , we see m is 201 so q=1, m =110 Ans E.

Re: When m is divided by 7, the remainder is 5. When m is divided by 13 [#permalink]

Show Tags

30 Aug 2017, 13:34

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.
_________________

When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m?

A. 5 B. 19 C. 61 D. 74 E. 110

We are given two properties about m: when m is divided by 7, the remainder is 5; further, when m is divided by 13, the remainder is 6. We can create the following two equations:

m = 7Q + 5

According to the above expression, m can be:

5, 12, 19, ...

m = 13z + 6

According to the above expression, m can be:

6, 19, 32, …

We can see that 19 is the smallest positive integer value of m that satisfies the properties. However, we are asked to find the largest integer less than 200 that satisfies the properties. In that case, we can add 19 to any number that is both divisible by 13 and 7, in other words, a number that is a multiple of both 13 and 7. Since the LCM of 13 and 7 is 13 x 7 = 91, the next value of m is 19 + 91 = 110, which happens to be the largest possible value of m that is still less than 200. (Note: the next value of m is 110 + 91 = 201, which is greater than 200.)

Alternate solution:

The problem is asking for the largest possible value less than 200 that satisfies the following properties: when m is divided by 7, the remainder is 5, and when m is divided by 13, the remainder is 6. We can check the largest number in the given answer choices first and work backward until we find the answer. So let’s check 110 first:

110/7 = 15 R 5 and 110/13 = 8 R 6

We see that 110 satisfies both properties, so 110 is the answer. . Answer: E
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...