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

It is currently 16 Nov 2018, 06:13

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

When m is divided by 9, the remainder is 2. When m is divide

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 419
When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post Updated on: 24 Mar 2014, 02:45
1
12
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

71% (02:11) correct 29% (02:12) wrong based on 288 sessions

HideShow timer Statistics

When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?

A. 47
B. 65
C. 103
D. 117
E. 164

OE:
Answer choice (E)
Nearest multiple of 9 to 164 = 18×9=162, leaving a remainder of 2.
Nearest multiple of 13 to 164 = 12×13 = 156, leaving a remainder of 8.
Thus 164 fits both conditions, and the greatest answer choice

Originally posted by goodyear2013 on 24 Mar 2014, 02:23.
Last edited by Bunuel on 24 Mar 2014, 02:45, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50617
Re: When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 24 Mar 2014, 02:53
4
4
goodyear2013 wrote:
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?

A. 47
B. 65
C. 103
D. 117
E. 164

OE:
Answer choice (E)
Nearest multiple of 9 to 164 = 18×9=162, leaving a remainder of 2.
Nearest multiple of 13 to 164 = 12×13 = 156, leaving a remainder of 8.
Thus 164 fits both conditions, and the greatest answer choice


When m is divided by 9, the remainder is 2 --> \(m=9q+2\) --> m can be 2, 11, 20, 29, 38, 47, ...
When m is divided by 13, the remainder is 8 --> \(m=13p+8\) --> m can be 8, 21, 34, 47, 60, 73, ...

There is a way to derive general formula for m (of a type \(m=dx+r\), where d is divisor and r is a remainder) based on above two statements:

Divisor d would be the least common multiple of above two divisors 9 and 13, hence \(d=117\) and the remainder r would be the first common integer in above two patterns, hence \(r=47\).

Therefore general formula based on both statements is \(m=117x+47\) --> n can be 47, 164, 211, ... Since m must be less than 200, then the greatest possible value of m is 164.

Answer: E.

More about deriving general formula for such problems at: manhattan-remainder-problem-93752.html#p721341

Hope it helps.
_________________

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

General Discussion
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 26 Mar 2014, 19:37
2
Looking at the choices, options B & D can be eliminated as they are divisible by 13

Starting from the highest number 164;

164 = 162 + 2 (162 divisible by 9)

164 = 156 + 8 (156 divisible by 13)

it fits the result

Answer = E
_________________

Kindly press "+1 Kudos" to appreciate :)

Retired Moderator
avatar
B
Joined: 17 Sep 2013
Posts: 344
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
GMAT ToolKit User Premium Member Reviews Badge
Re: When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 05 Jul 2014, 07:09
An obvious approach would be to start with the largest number
Fortunately it satisfies both the remainder criteria..E it is
_________________

Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..:P

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3120
Location: Canada
Re: When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 23 Oct 2015, 12:29
3
goodyear2013 wrote:
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?

A. 47
B. 65
C. 103
D. 117
E. 164



I would probably go with Bunuel's solution, but here's another approach:

There's a nice rule that says "If a number is divisible by 9, the sum of its digits will be divisible by 9"
For example, we know that 551008 is divisible by 9, because the sum of its digits equals 18, and 18 is divisible by 9

We're told that when m is divided by 9, the remainder is 2.
So, my is TWO GREATER than some multiple of 9.

So, for a possible value of m to meet this condition, all we need to do is subtract 2 from that value and see if it is divisible by 9.
Let's check the answer choices:

A. 47 - 2 = 45 This is divisible by 9, so m MIGHT equal 47
B. 65 - 2 = 63 This is divisible by 9, so m MIGHT equal 65
C. 103 - 2 = 101 This is NOT divisible by 9, so ELIMINATE C
D. 117 - 2 = 115 This is NOT divisible by 9, so ELIMINATE D
E. 164 - 2 = 162 This is divisible by 9, so m MIGHT equal 164

Let's start with the largest answer choice (E) and see if it meets the second condition (When m is divided by 13, the remainder is 8.)
164 divided by 13 = 12 with remainder 8
DONE

Answer: E

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image

Intern
Intern
avatar
B
Joined: 01 May 2017
Posts: 13
Re: When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 03 Jun 2017, 04:18
This question can be solved just going by option ,

greatest value , start from E and you have ur answer ...easiest and sound way
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1113
When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 03 Jun 2017, 13:00
goodyear2013 wrote:
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 8. If 1 < m < 200, what is the greatest possible value of m?

A. 47
B. 65
C. 103
D. 117
E. 164


assume difference of 1 between m/9 and m/13 quotients
(m-2)/9-(m-8)/13=1
4m=71 :(
assume difference of 2
4m=71+117=188 :)
m=47
47+9*13=164
E
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8784
Premium Member
Re: When m is divided by 9, the remainder is 2. When m is divide  [#permalink]

Show Tags

New post 06 Sep 2018, 00:37
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: When m is divided by 9, the remainder is 2. When m is divide &nbs [#permalink] 06 Sep 2018, 00:37
Display posts from previous: Sort by

When m is divided by 9, the remainder is 2. When m is divide

  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®.