BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

When 10 is divided by the positive integer n,

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Mon Dec 10, 2007 1:35 pm
Location: London, UK
Thanked: 19 times
GMAT Score:680
by II » Sun Aug 24, 2008 11:23 am
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

Please illustrate your logic and working out.

Thanks,
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 315
Joined: Thu Aug 17, 2006 10:43 pm
Thanked: 23 times

by Suyog » Sun Aug 24, 2008 11:31 am
plugging n with the options given...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 829
Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members
Location: INDIA
Thanked: 84 times

Re: When 10 is divided by the positive integer n,

by sudhir3127 » Sun Aug 24, 2008 11:40 am
II 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

Please illustrate your logic and working out.

Thanks,
divi

C.

Dividend = Quotient x Divisor + Remainder

any options less than 10 , quotient will be 1

so its
n*1+ n-4 =10
2n-4 =10
n =7

Hope that helps
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Mon Dec 10, 2007 1:35 pm
Location: London, UK
Thanked: 19 times
GMAT Score:680

by II » Sun Aug 24, 2008 2:51 pm
Suyog wrote:plugging n with the options given...
Thanks ... and this is the approach I used ... was interested in learning about other alternative approaches.

Thanks.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Sat Oct 03, 2009 8:57 pm

by Baten80 » Fri Mar 04, 2011 10:29 pm
sudhir3127 wrote:
II 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

Please illustrate your logic and working out.

Thanks,
divi

C.

Dividend = Quotient x Divisor + Remainder

any options less than 10 , quotient will be 1

so its
n*1+ n-4 =10
2n-4 =10
n =7

Hope that helps
any options less than 10 , quotient will be 1
But here option is 10, which is not less then 10 but quotient is 1. What is the explanation?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 436
Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members
Thanked: 72 times

by manpsingh87 » Fri Mar 04, 2011 10:43 pm
II 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

Please illustrate your logic and working out.

Thanks,
Numerator= Quotient* Denominator + remainder.

10 = Kn + n-4;
14 = (k+1)n;
14/k+1 = n;

now as n should be integer, therefore for k=6; n=7

here important thing to note is k can take any value.!!!!
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Sat Mar 05, 2011 12:00 am
II 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

Please illustrate your logic and working out.

Thanks,

Remember, Dividend = Divisor × Quotient + Remainder

Remainder in arithmetic is a non negative integer, and so are the Dividend and Quotient, hence n - 4 ≥ 0 or n ≥ 4.


We further have
10 = q × n + (n - 4) or n (q + 1) = 14.

Here is where we must play further logic; the product of two positive integers n and (q + 1) is 14, and n ≥ 4, which means that n can neither be 1 nor 2 as a possible factor of 14, and yes, n can either be 14 or 7 as a possible factor of 14. Since 14 is not among the choices, pick [spoiler]7



C[/spoiler]
Last edited by sanju09 on Sat Mar 05, 2011 12:25 am, edited 1 time in total.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 613
Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members
Location: madrid
Thanked: 171 times
GMAT Score:790

by kevincanspain » Sat Mar 05, 2011 12:07 am
And also note that the Remainder is always less than the Divisor, hence

n - 4 < 10 or n < 14

Note that when 10 is divided by 14, the remainder is 10, i.e. 4 less than 14. This explains the word could. Be careful not to confuse dividend with divisor
Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members
Location: India
Thanked: 267 times
GMAT Score:760

by sanju09 » Sat Mar 05, 2011 12:26 am
kevincanspain wrote:And also note that the Remainder is always less than the Divisor, hence

n - 4 < 10 or n < 14

Note that when 10 is divided by 14, the remainder is 10, i.e. 4 less than 14. This explains the word could. Be careful not to confuse dividend with divisor
Thanks kevincanspain, that was an error, now edited :)
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jan 02, 2018 7:29 am
II 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
Let's test each answer choice:

A) n = 3

10/3 = remainder 1, which does not equal 3 - 4.

B) n = 4

10/4 = remainder 2, which does not equal 4 - 4.

C) n = 7

10/7 = remainder 3, which does equal 7 - 4.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1