Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Aug 2014, 12:22

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

When 10 is divided by the positive integer n, the remainder

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 10 Mar 2008
Posts: 376
Followers: 3

Kudos [?]: 46 [1] , given: 0

GMAT Tests User
When 10 is divided by the positive integer n, the remainder [#permalink] New post 15 Sep 2008, 13:33
1
This post received
KUDOS
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

90% (01:40) correct 10% (00:53) wrong based on 217 sessions
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ?

A) 3
B) 4
C) 7
D) 8
E) 12
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 11 Jan 2008
Posts: 54
Followers: 0

Kudos [?]: 14 [0], given: 0

Re: PS: Remainder Theory [#permalink] New post 15 Sep 2008, 16:08
back solving is easier for this one.

10/7 gives a remainder of 3. n-4 = 7-4 = 3
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
Re: PS: Remainder Theory [#permalink] New post 16 Sep 2008, 06:18
10=NK+N-4; assume K=1

10=2N-4

14=2N. N has to be a multiple of 7...

C it is..
SVP
SVP
avatar
Joined: 21 Jul 2006
Posts: 1550
Followers: 8

Kudos [?]: 192 [0], given: 1

GMAT Tests User
Re: PS: Remainder Theory [#permalink] New post 17 Sep 2008, 06:04
vksunder wrote:
fresinha12 - I did the same way as you had described. But is it safe to assume that K=1?



well, since we can never have the denominator to be zero, otherwise the fraction will be undefined. so it makes sense to start off with k=1. If that doesn't work, then you just have to keep increasing the value of k until you can match your answer with the correct answer choice.
SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1580
Followers: 12

Kudos [?]: 180 [0], given: 0

GMAT Tests User
Re: PS: Remainder Theory [#permalink] New post 17 Sep 2008, 23:18
I approached as follows.

10 = nx + n-4 for x = 0,1,2,3,4......
or, n(x+1) = 14
or, n = 14/(x+1)

For x = 0, n = 14, for x = 1, n = 7, x cannot be 2,3,4,5.
For x = 6, n = 2. x cannot be greater than 6.

Hence, possible values of n are 14, 7, 2. Answer choice has 7. Hence, 7 is the answer.
Manager
Manager
avatar
Joined: 30 May 2010
Posts: 191
Followers: 3

Kudos [?]: 41 [0], given: 32

GMAT Tests User
Number properties question from QR 2nd edition PS 164 [#permalink] New post 17 Jun 2010, 23:12
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?
Manager
Manager
avatar
Joined: 07 Oct 2006
Posts: 73
Location: India
Followers: 1

Kudos [?]: 6 [0], given: 3

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 17 Jun 2010, 23:56
As per my approach, it is easy to reach the solution by going thorough each one of the options.
You can eliminate 12,8,4 and 3 at one look. Then you just need to check for 7. It took me less than 1 minute to get to the answer. So that should be fine I guess.
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3362

Kudos [?]: 24464 [4] , given: 2677

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 18 Jun 2010, 00:58
4
This post received
KUDOS
Expert's post
jpr200012 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?


Algebraic approach:

THEORY:
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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so 10=nq+(n-4) and also n-4\geq{0} or n\geq{4} (remainder must be non-negative).

10=nq+n-4 --> 14=n(q+1) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
Posts: 1855
Followers: 336

Kudos [?]: 1361 [0], given: 194

GMAT ToolKit User GMAT Tests User
Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 18 Jun 2010, 05:29
It says that the remainder when you divide 10 by n is n-4

This basically can be translated into the following statement algebraically:

10 = kn + (n-4)

This is simplified as follows:

10 = kn + n -4 = n *(k+1) - 4

Further simplifying:

10 + 4 = n*(k+1)

14 = n*(k+1)

7*2 = n*(k+1)


So n can be 7 or 2.

Only 7 is listed as an option here, so the answer is C. Hope this helps!




jpr200012 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3362

Kudos [?]: 24464 [0], given: 2677

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 18 Jun 2010, 05:46
Expert's post
whiplash2411 wrote:
It says that the remainder when you divide 10 by n is n-4

This basically can be translated into the following statement algebraically:

10 = kn + (n-4)

This is simplified as follows:

10 = kn + n -4 = n *(k+1) - 4

Further simplifying:

10 + 4 = n*(k+1)

14 = n*(k+1)

7*2 = n*(k+1)


So n can be 7 or 2.

Only 7 is listed as an option here, so the answer is C. Hope this helps!


n cannot be 2 as in this case remainder =n-4=-2<0 and remainder is always non-negative (also notice that 10/2 has no remainder and n-4=-2, though n can also be 14 --> 10=14*0+(14-4)).

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Ms. Big Fat Panda
Ms. Big Fat Panda
User avatar
Status: Biting Nails Into Oblivion
Joined: 09 Jun 2010
Posts: 1855
Followers: 336

Kudos [?]: 1361 [0], given: 194

GMAT ToolKit User GMAT Tests User
Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 18 Jun 2010, 05:52
Oh, yeah, that's right. I just saw the 7 and 2, and looked at the answer choices and chose 7.

Thanks, Bunuel. Your explanation will come in handy in case both 2 and 7 were listed as answer choices! :-D
Director
Director
avatar
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 25 [0], given: 7

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 16 Jul 2010, 03:22
Quote:
remainder is always non-negative


Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3362

Kudos [?]: 24464 [0], given: 2677

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 16 Jul 2010, 06:14
Expert's post
nonameee wrote:
Quote:
remainder is always non-negative


Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder


This has nothing to do with GMAT.

GMAT Prep definition of the remainder:

If a and d are positive integers, there exists unique integers q and r, such that a = qd + r and 0\leq{r}<d. q is called a quotient and r is called a remainder.

Also EVERY GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

So trust me: remainder is always non-negative and less than divisor for GMAT - 0\leq{r}<d.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 25 [0], given: 7

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 16 Jul 2010, 13:00
Thanks for clarification. But you can use that property (negative remainder) to solve remainder problems (as it has been done in several posts).
Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 932
Followers: 11

Kudos [?]: 190 [0], given: 123

Reviews Badge
Re: QR. 164 Remainder [#permalink] New post 05 Mar 2011, 00:24
If division by n leaves reminder. Then
i.e. Dividend - Remainder is a multiple of divider.
Here 10 -(n-4) must be a multiple of n.

Or Is [10 - (n-4)] / n = integer?

Now plug in the values of n from the options.

A - n-4 will give negative remainder. Illogical
B - (10-0)/4 is not integer
C - (10-3)/7 is integer
D - (10-4)/8 is not integer
E - (10-8)/12 is not integer

Answer C.

Baten80 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ?

A) 3
B) 4
C) 7
D) 8
E) 12
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2048
Followers: 128

Kudos [?]: 898 [0], given: 376

GMAT Tests User
Re: QR. 164 Remainder [#permalink] New post 05 Mar 2011, 00:44
10=nQ+n-4 where Q is the quotient

n(Q+1)=14, where n and Q are both integers.

Factors of 14;
n*(Q+1)
1*14; n=1, Q=13; Not possible because 1 won't leave any remainder with 10
2*7; n=2, Q=6; Not possible because 2 won't leave any remainder with 10
7*2; n=7, Q=1; Possible
14*1; n=14, Q=0; Possible

So; n can be 7 or 14.

Ans: "C"
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 81 [0], given: 42

GMAT Tests User
Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 06 Mar 2011, 14:04
Nice explanation there Bunuel.


Bunuel wrote:
jpr200012 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?


Algebraic approach:

THEORY:
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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so 10=nq+(n-4) and also n-4\geq{0} or n\geq{4} (remainder must be non-negative).

10=nq+n-4 --> 14=n(q+1) --> n is an factor of 14 and \geq{4} --> n can be 7 or 14.

Answer: C.

Hope it's clear.
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 81 [0], given: 42

GMAT Tests User
Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 06 Mar 2011, 14:48
I thought of the same , why cant a remainder be negative?

I guess in some cases , as Bunel is suggesting we need to make an assumption that we are dealing with just positive integers.


nonameee wrote:
Quote:
remainder is always non-negative


Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder

Last edited by Spidy001 on 06 Mar 2011, 15:27, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3362

Kudos [?]: 24464 [0], given: 2677

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 06 Mar 2011, 14:55
Expert's post
Spidy001 wrote:
I thought of the same , why cant a remainder be negative?

I guess in some cases , as Bunel is suggesting we need an assumption that we are dealing with just positive integers.


nonameee wrote:
Quote:
remainder is always non-negative


Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder


It's not an assumption.

Remainder is a non-negative by definition (at least on the GMAT).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 81 [0], given: 42

GMAT Tests User
Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 06 Mar 2011, 15:41
Bunuel,

I know in this case we don't have to make any assumption, because the question clearly states these are two positive integers.


i was referring more to scenarios like negative number division

-25 /7

-25 = 7(-3)+(-4)

Here remainder is -4 which is negative.

so lets say if question is like x,y are integers x/y . we cannot generalize and say remainder >=0 ,unless we assume that we are only talking about positive integers.




nonameee wrote:
Quote:
remainder is always non-negative


Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder
[/quote]

It's not an assumption.

Remainder is a non-negative by definition (at least on the GMAT).[/quote]
Re: Number properties question from QR 2nd edition PS 164   [#permalink] 06 Mar 2011, 15:41
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic When 10 is divided by the positive integer n, the remainder Bunuel 2 14 Mar 2014, 02:18
What is the remainder when positive Integer n is divided by GmatInstinct 2 25 Sep 2006, 16:01
If r is the remainder when positive integer n is divided by wshaffer 4 18 Sep 2006, 16:43
What is the remainder when the positive integer n is divided sperumba 9 18 Jan 2006, 18:58
What is the remainder when the positive integer n is divided mandy 9 03 Aug 2005, 05:35
Display posts from previous: Sort by

When 10 is divided by the positive integer n, the remainder

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 34 posts ] 



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

Powered by phpBB © phpBB Group and phpBB SEO

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®.