It is currently 19 Apr 2018, 19:54

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

Events & Promotions in June
Open Detailed Calendar

When 15 is divided by the positive integer k, the remainder

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

Hide Tags

Intern
Intern
avatar
Joined: 20 Jun 2013
Posts: 4
When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post Updated on: 09 Apr 2014, 02:01
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:01) correct 43% (00:52) wrong based on 315 sessions

HideShow timer Statistics

When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?

A) 1
B) 2
C) 3
D) 4
E) 5
[Reveal] Spoiler: OA

Originally posted by sinchicodo on 08 Apr 2014, 22:27.
Last edited by Bunuel on 09 Apr 2014, 02:01, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8024
Location: Pune, India
Re: When 15 is divided by the positive integer k? remainder is ? [#permalink]

Show Tags

New post 08 Apr 2014, 22:42
4
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
sinchicodo wrote:
When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?

A) 1
B) 2
C) 3
D) 4
E) 5


When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3.
It also means that 12 is completely divisible by k.

Factors of 12 are 1, 2, 3, 4, 6, 12

Out of these, k can be 4, 6 and 12.

Answer (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 20 Jun 2013
Posts: 4
Re: When 15 is divided by the positive integer k? remainder is ? [#permalink]

Show Tags

New post 08 Apr 2014, 22:49
VeritasPrepKarishma wrote:
sinchicodo wrote:
When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?

A) 1
B) 2
C) 3
D) 4
E) 5


When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3.
It also means that 12 is completely divisible by k.

Factors of 12 are 1, 2, 3, 4, 6, 12

Out of these, k can be 4, 6 and 12.

Answer (C)


why does it mean that "12 is completely divisible by k?"
Expert Post
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8024
Location: Pune, India
Re: When 15 is divided by the positive integer k? remainder is ? [#permalink]

Show Tags

New post 08 Apr 2014, 23:00
sinchicodo wrote:
VeritasPrepKarishma wrote:
sinchicodo wrote:
When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?

A) 1
B) 2
C) 3
D) 4
E) 5


When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3.
It also means that 12 is completely divisible by k.

Factors of 12 are 1, 2, 3, 4, 6, 12

Out of these, k can be 4, 6 and 12.

Answer (C)


why does it mean that "12 is completely divisible by k?"


Since the remainder is 3, it means 3 is extra. If you remove 3 from 15, whatever is left is completely divisible by k. You should check out these posts for theory on divisibility and remainders:
http://www.veritasprep.com/blog/2011/04 ... unraveled/
http://www.veritasprep.com/blog/2011/04 ... y-applied/
http://www.veritasprep.com/blog/2011/05 ... emainders/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44566
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 09 Apr 2014, 02:04
2
This post received
KUDOS
Expert's post
sinchicodo wrote:
When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?

A) 1
B) 2
C) 3
D) 4
E) 5


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).

When 15 is divided by the positive integer k, the remainder is 3 --> \(15=kq+3\), where \(k>3\).

From above: \(15=kq+3\) --> \(kq=12\) --> k is a factor of 12 greater than 3, thus k can be 4, 6, or 12.

Answer: C.

Similar question to practice: if-x-y-represents-the-remainder-that-results-when-the-po-169530.html

Theory on remainders problems: remainders-144665.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199

_________________

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

Manager
Manager
User avatar
Joined: 03 Jan 2015
Posts: 66
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 30 Jan 2015, 19:18
VeritasPrepKarishma wrote:
sinchicodo wrote:
When 15 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?

A) 1
B) 2
C) 3
D) 4
E) 5


When 15 is divided by k, remainder is 3 i.e. there are 3 balls leftover after grouping. so k must be greater than 3.
It also means that 12 is completely divisible by k.

Factors of 12 are 1, 2, 3, 4, 6, 12

Out of these, k can be 4, 6 and 12.

Answer (C)


Hi Karisma,

Thank you for the posts. I also read your Veritas blog on "grouping marbles" on this topic. However, I still cannot understand why K > 3. Based on grouping marbles analogy, for 15 marbles, I can have a remainder of 3 for:

2 groups: 6 marbles each
6 groups: 2 marbles each
4 groups: 3 marbles each
3 groups 4 marbles each
1 group: 12 marbles

or for Bunuel's formula 15 = KV + 3, where K can be a number for any of the above marble-group combination.

Can your explanation be made even more simpler to understand why K > 3?

Thank you,

TO
Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11489
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 30 Jan 2015, 20:19
1
This post received
KUDOS
Expert's post
Hi thorinoakenshield,

When dealing with a 'remainder' question, there's a relationship between what you 'divide by' and the 'possible remainders'

If you're supposed to end up with a remainder of 3, then you CANNOT be dividing by 1, 2 or 3 (since dividing by any of those numbers CANNOT yield a reminder of 3):

For example:

17/1 = 17r0

17/2 = 8r1

17/3 = 5r2

To have a remainder of 3, we need to divide by a number that is GREATER than 3....

eg 7/4 = 1r3

When combined with the possibilities that Karishma defined (1,2,3,4,6,12), the ONLY values that fit both restrictions are 4, 6 and 12....

15/4 = 3r3
15/6 = 2r3
15/12 = 1r3

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Manager
Manager
User avatar
Joined: 03 Jan 2015
Posts: 66
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
GMAT ToolKit User
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 30 Jan 2015, 20:52
EMPOWERgmatRichC wrote:
Hi thorinoakenshield,

When dealing with a 'remainder' question, there's a relationship between what you 'divide by' and the 'possible remainders'

If you're supposed to end up with a remainder of 3, then you CANNOT be dividing by 1, 2 or 3 (since dividing by any of those numbers CANNOT yield a reminder of 3):

For example:

17/1 = 17r0

17/2 = 8r1

17/3 = 5r2

To have a remainder of 3, we need to divide by a number that is GREATER than 3....

eg 7/4 = 1r3

When combined with the possibilities that Karishma defined (1,2,3,4,6,12), the ONLY values that fit both restrictions are 4, 6 and 12....

15/4 = 3r3
15/6 = 2r3
15/12 = 1r3

GMAT assassins aren't born, they're made,
Rich


Hi Rich,

Thank you! It makes sense now.

TO
Intern
Intern
User avatar
B
Joined: 29 Dec 2017
Posts: 33
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GPA: 3.25
WE: Marketing (Telecommunications)
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 02 Apr 2018, 08:05
Hi there,
I think the question should have constraints such as k<15. Otherwise 15/20 = 3/4 - leaves us the remainder of 3, so K is unlimited.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44566
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 02 Apr 2018, 08:39
1
This post received
KUDOS
Expert's post
Hero8888 wrote:
Hi there,
I think the question should have constraints such as k<15. Otherwise 15/20 = 3/4 - leaves us the remainder of 3, so K is unlimited.


15 divided by 20 does not give the remainder of 3 as stated in the stem. As far as remainders are concerned, 15/20 is not the same as 3/4, you cannot reduce like this: 15 divided by 20 gives the remainder of 15 but 3 divided by 4 gives the remainder of 3.
_________________

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

Intern
Intern
User avatar
B
Joined: 29 Dec 2017
Posts: 33
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GPA: 3.25
WE: Marketing (Telecommunications)
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 02 Apr 2018, 09:32
Bunuel wrote:
Hero8888 wrote:
Hi there,
I think the question should have constraints such as k<15. Otherwise 15/20 = 3/4 - leaves us the remainder of 3, so K is unlimited.


15 divided by 20 does not give the remainder of 3 as stated in the stem. As far as remainders are concerned, 15/20 is not the same as 3/4, you cannot reduce like this: 15 divided by 20 gives the remainder of 15 but 3 divided by 4 gives the remainder of 3.


Got it! I didn't know about the fine point tested on GMAT. Thank you!
Manager
Manager
avatar
B
Joined: 08 Sep 2016
Posts: 56
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 02 Apr 2018, 13:16
15/k = q +3
15=kq+3
12=kq

prime factors for 12 = 2*2*3

Different values that fit: 2*2, 2*3, 4*3 -> 4,6,12

answer C
1 KUDOS received
Intern
Intern
avatar
B
Joined: 02 Oct 2016
Posts: 25
Reviews Badge CAT Tests
Re: When 15 is divided by the positive integer k, the remainder [#permalink]

Show Tags

New post 08 Apr 2018, 06:57
1
This post received
KUDOS
Factors of 12 are 1, 2, 3, 4, 6, 12

Out of these, k can be 4, 6 and 12.

Answer (C)
Re: When 15 is divided by the positive integer k, the remainder   [#permalink] 08 Apr 2018, 06:57
Display posts from previous: Sort by

When 15 is divided by the positive integer k, the remainder

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.