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

It is currently 02 Oct 2014, 04:32

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:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23079
Followers: 3543

Kudos [?]: 27355 [0], given: 2734

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

Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 770
Followers: 14

Kudos [?]: 82 [0], given: 42

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]
Director
Director
avatar
Joined: 29 Nov 2012
Posts: 929
Followers: 12

Kudos [?]: 285 [0], given: 543

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 09 Jan 2013, 03:02
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.



So in this step are we substituting q=0,1 etc or is it something else?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: When 10 is divided by the positive integer n, the remainder [#permalink] New post 10 Jan 2013, 13:55
backsolving works best.
Senior Manager
Senior Manager
avatar
Joined: 08 Jun 2010
Posts: 454
Followers: 0

Kudos [?]: 28 [0], given: 39

Re: When 10 is divided by the positive integer n, the remainder [#permalink] New post 27 Feb 2013, 02:19
I want to follow this question.
hard one of course.
Intern
Intern
avatar
Joined: 09 Oct 2012
Posts: 13
Followers: 0

Kudos [?]: 2 [0], given: 14

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 21 Sep 2013, 08:10
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.


Hi Bunuel,
I also considered n=7,14 as the only two options since the remainder has to be non-negative. However, the following official explanation (Quant Review 2nd edition, PS 164) confused me:

"10 = qn + (n- 4}. So, 14 = qn + n = n(q + 1). This means that n must be a factor of 14 and so n= 1, n = 2, n = 7, or n = 14 since n is a positive integer and the only positive integer factors of 14 are 1, 2, 7, and 14. The only positive integer factor of 14 given in the answer choices is 7."

Here n=1 and n=2 are considered as possible values for n even though that will make the remainder n-4 negative. :shock:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23079
Followers: 3543

Kudos [?]: 27355 [0], given: 2734

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 21 Sep 2013, 08:31
Expert's post
panda007 wrote:
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.


Hi Bunuel,
I also considered n=7,14 as the only two options since the remainder has to be non-negative. However, the following official explanation (Quant Review 2nd edition, PS 164) confused me:

"10 = qn + (n- 4}. So, 14 = qn + n = n(q + 1). This means that n must be a factor of 14 and so n= 1, n = 2, n = 7, or n = 14 since n is a positive integer and the only positive integer factors of 14 are 1, 2, 7, and 14. The only positive integer factor of 14 given in the answer choices is 7."

Here n=1 and n=2 are considered as possible values for n even though that will make the remainder n-4 negative. :shock:


These values are considered solely based on 14=n(q+1).
_________________

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

Intern
Intern
avatar
Joined: 09 Oct 2012
Posts: 13
Followers: 0

Kudos [?]: 2 [0], given: 14

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 21 Sep 2013, 08:47
Bunuel wrote:
These values are considered solely based on 14=n(q+1).


So, I guess the official explanation is incomplete in the sense that it doesn't take into account the properties of remainders. I am surprised n-4>=0 wasn't taken into account but hope it is a mistake rather than the possibility that the remainder rule is not strictly applicable.
Intern
Intern
avatar
Joined: 01 Jul 2013
Posts: 19
Schools: LBS MIF '15
Followers: 0

Kudos [?]: 16 [0], given: 16

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 25 Sep 2013, 07:09
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.


I got stuck when I got to 14=n(q+1) - so do we just completely ignore the 'q'? and why do we ignore the 'q'? can't q be something like 13 and 'n' becomes any random number? what am I missing here?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23079
Followers: 3543

Kudos [?]: 27355 [0], given: 2734

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 25 Sep 2013, 07:32
Expert's post
bulletpoint wrote:
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.


I got stuck when I got to 14=n(q+1) - so do we just completely ignore the 'q'? and why do we ignore the 'q'? can't q be something like 13 and 'n' becomes any random number? what am I missing here?


We don't ignore q, we are just not interested in it. q is a quotient, so is a non-negative integer, thus we have 14=n(q+1)=integer*integer --> both multiples are factors of 14.

Does this make sense?
_________________

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

Intern
Intern
avatar
Joined: 01 Jul 2013
Posts: 19
Schools: LBS MIF '15
Followers: 0

Kudos [?]: 16 [0], given: 16

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 26 Sep 2013, 01:56
Bunuel wrote:
bulletpoint wrote:

I got stuck when I got to 14=n(q+1) - so do we just completely ignore the 'q'? and why do we ignore the 'q'? can't q be something like 13 and 'n' becomes any random number? what am I missing here?


We don't ignore q, we are just not interested in it. q is a quotient, so is a non-negative integer, thus we have 14=n(q+1)=integer*integer --> both multiples are factors of 14.

Does this make sense?


why do both 'n' and '(q+1)' have to be factors of 14? if 'q+1' is a factor of 14, then 'n' need not be a factor of 14 for the equation 14=n(q+1) to be true, right?

or is it that for questions of these types - since we are only interested in what 'n' is - we just completely ignore the '(q+1)' part?

EDIT: Just took a look at what you said again and I think I get it. Please correct me if I'm wrong:

14=n(q+1) means 'n' OR '(q+1)' can equal 1,2,7,14 to make the equation true, and since 'n' has to be greater or equal to 4 because remainder must be non-negative, it can only be true that 'n' equals 7 or 14, and because the answer only has 7, this would be the correct answer.

Last edited by bulletpoint on 26 Sep 2013, 02:00, edited 1 time in total.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23079
Followers: 3543

Kudos [?]: 27355 [0], given: 2734

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 26 Sep 2013, 01:59
Expert's post
bulletpoint wrote:
Bunuel wrote:
bulletpoint wrote:

I got stuck when I got to 14=n(q+1) - so do we just completely ignore the 'q'? and why do we ignore the 'q'? can't q be something like 13 and 'n' becomes any random number? what am I missing here?


We don't ignore q, we are just not interested in it. q is a quotient, so is a non-negative integer, thus we have 14=n(q+1)=integer*integer --> both multiples are factors of 14.

Does this make sense?


why do both 'n' and '(q+1)' have to be factors of 14? if 'q+1' is a factor of 14, then 'n' need not be a factor of 14 for the equation 14=n(q+1) to be true, right?

or is it that for questions of these types - since we are only interested in what 'n' is - we just completely ignore the '(q+1)' part?


Again we do NOT ignore q+1.

Next, 14 = n(q+1) = integer*integer:
14/n = q+1 = integer --> n is a factor of 14.
14/(q+1) = n = integer --> q+1 is a factor of 14.
_________________

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

Current Student
avatar
Joined: 26 Sep 2013
Posts: 232
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 37 [0], given: 40

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 23 Oct 2013, 17:42
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.


could you clarify the highlighted portion? is n being 7 because 14=2*7?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23079
Followers: 3543

Kudos [?]: 27355 [0], given: 2734

Re: Number properties question from QR 2nd edition PS 164 [#permalink] New post 23 Oct 2013, 23:20
Expert's post
AccipiterQ wrote:
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) --> as 14=1*14=2*7 and \geq{4} then --> n can be 7 or 14.

Answer: C.

Hope it's clear.


could you clarify the highlighted portion? is n being 7 because 14=2*7?


Yes, we know that n\geq{4} and 14=n*(positive \ integer). Now, 14=1*14=2*7, thus n can be 7 or 14.

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

Re: Number properties question from QR 2nd edition PS 164   [#permalink] 23 Oct 2013, 23:20
    Similar topics Author Replies Last post
Similar
Topics:
1 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
When a positive integer n is divided by 3, the remainder is asaf 3 14 Jul 2007, 13:07
What is the remainder when the positive integer n is divided Balvinder 5 24 May 2007, 05:46
What is the remainder when positive Integer n is divided by GmatInstinct 2 25 Sep 2006, 16:01
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   Previous    1   2   [ 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®.