GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Dec 2018, 20:07

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

When m is divided by 7, the remainder is 5. When m is divided by 13

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51121
When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 17 Aug 2016, 11:20
1
13
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (01:23) correct 24% (01:59) wrong based on 302 sessions

HideShow timer Statistics

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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Intern
Intern
avatar
B
Joined: 20 Sep 2011
Posts: 18
Concentration: Operations, International Business
Schools: Ross '17, ISB '16, NUS '17
GMAT 1: 640 Q40 V35
GMAT ToolKit User Reviews Badge
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 20 Aug 2016, 09:51
4
3
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.
General Discussion
Senior Manager
Senior Manager
avatar
Joined: 23 Apr 2015
Posts: 305
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 17 Aug 2016, 12:00
1
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

Answer is E.
I started with E.110 and it fits the bill . 105 is divisible by 7 and 104 is divisible by 13. so it's E.

Modular approach would be the proper way, but this worked at first attempt.
Intern
Intern
User avatar
B
Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 17 Aug 2016, 12:57
110 is the answer. As 110 is the largest of the five answer choices you can start with it.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1128
When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 17 Aug 2016, 17:54
1
4
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
Senior Manager
Senior Manager
avatar
Joined: 23 Apr 2015
Posts: 305
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 17 Aug 2016, 19:44
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.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1128
When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 17 Aug 2016, 20:26
4
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
Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 191
Location: Ghana
Premium Member
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 18 Aug 2016, 10:05
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


You can also get to the answer by backsolving using the answer choices.

Since we want the greatest possible value of m within the given range, let's start with option E

Option E
110/7 = 15 + r5
110/13 = 8 + r6 end here, no need to continue! We have gotten what we want.

m = 110

Answer: E
_________________

Kindly press kudos if you find my post helpful

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 18 Aug 2016, 21:12
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


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.

For more on this concept, check: http://www.veritasprep.com/blog/2011/05 ... s-part-ii/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 05 Sep 2017, 17:03
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


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

GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 536
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 20 Nov 2018, 17:37
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

\(? = {m_{\,\max }}\,\,\,\left( {1 < m < 200} \right)\,\,{\text{such}}\,\,{\text{that}}\,\,\,\,\left\{ \begin{gathered}
m = 7Q + 5\,\,\,\left( 1 \right)\,\, \hfill \\
m = 13K + 6\,\,\,\left( 2 \right) \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\left( {Q,K\,\,\,{\text{ints}}} \right)\)

\(\left\{ \begin{gathered}
\left( 1 \right) \cdot 13\,\,\,\, \Rightarrow \,\,\,\,13m = 7 \cdot 13Q + 65 \hfill \\
\left( 2 \right) \cdot 7\,\,\,\,\,\, \Rightarrow \,\,\,\,7m = 7 \cdot 13K + 42 \hfill \\
\end{gathered} \right.\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,6m = 7 \cdot 13\left( {Q - K} \right) + 23\)

\(\left\{ \begin{gathered}
\,7m = 7 \cdot 13K + 42 \hfill \\
\,6m = 7 \cdot 13\left( {Q - K} \right) + 23 \hfill \\
\end{gathered} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,m = 7 \cdot 13\left( {2K - Q} \right) + 19\)

\(\left\{ \begin{gathered}
\,m = 91J + 19 \hfill \\
\,1 < m < 200 \hfill \\
\end{gathered} \right.\,\,\,\,\left( {J\,\,\operatorname{int} } \right)\,\,\,\, \Rightarrow \,\,\,\,\,{J_{\max }} = 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {m_{\,\max }} = 91 + 19 = 110\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

Manager
Manager
avatar
B
Joined: 13 Nov 2018
Posts: 60
Location: India
GMAT 1: 700 Q51 V32
CAT Tests
Re: When m is divided by 7, the remainder is 5. When m is divided by 13  [#permalink]

Show Tags

New post 28 Nov 2018, 07:44
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



We can do backsolving to reach to correct answer here rather than using remainder formula
We need to make sure any answer choice which satisfies above 2 condition is the right answer

As 110 is largest number in answer choices , start with E

110 when divide by 7 , remainder is 5, 110 when divided by 13, remiander 6, bingo, right answer within 20 seconds
_________________

It seems Kudos button not working correctly with all my posts...

Please check if it is working with this post......

is it?....

Anyways...Thanks for trying :cool:

GMAT Club Bot
Re: When m is divided by 7, the remainder is 5. When m is divided by 13 &nbs [#permalink] 28 Nov 2018, 07:44
Display posts from previous: Sort by

When m is divided by 7, the remainder is 5. When m is divided by 13

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.