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 →

DIVISIBILITY AND REMAINDERS

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Tue Nov 10, 2009 9:29 pm
Thanked: 1 times

by RoadtoIVY » Tue Nov 17, 2009 1:52 pm
N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20

1) is sufficient: Since N+1 is divisible by 3, N can be 2, 5, 8, 11 .... Let's try each one of them
N=2, then 4+7N = 4+14 = 18 >> 18 div 3 = remainder = 0
Similarly you get 0, if you try N = 5,8,11,14...

2) not sufficient since N>20 means, N can be 21,22,23,24...etc which does not give the same remainder.

Hope it heps.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 75
Joined: Thu Aug 20, 2009 11:55 am
Location: vancouver, B.C
GMAT Score:640

by hpgmat » Tue Nov 17, 2009 3:49 pm
THANK YOU. I GUESS PLUGGING IN NUMBERS IS NOT A BAD STRATEGY AFTER ALL
Will Win
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Mon May 12, 2008 12:26 pm
Thanked: 3 times

by adam15 » Tue Nov 17, 2009 8:05 pm
4+7N=3*c+R where c is an integer.(1)
1+N+3+6N=3*c+R
1+N=-3-6N+3*c+R
1+N=3*(c-2N)+R-3
by 1 we know that N+1=3*d where d is an integer
then we know that R-3=0 then R=3.
subsituting in (1)
yields 4+7*N=3*(c+1)
put c+1=e
4+7*N=3d
reminder is 0
then 1 is sufficient
2 is not
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Oct 24, 2009 4:43 pm
Thanked: 22 times
GMAT Score:710

by palvarez » Tue Nov 17, 2009 10:59 pm
hpgmat wrote:N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20
Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.

4+7n = r (3)

1 + n = r (3)

1. n +1 = 0 (mod 3)
n = 2 (mod 3)
r = n+1 (mod 3) = 3 (mod 3) = 0 Sufficient.

2. n > 20, we need to know n (mod 3). Useless.

A is sufficient.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 75
Joined: Thu Aug 20, 2009 11:55 am
Location: vancouver, B.C
GMAT Score:640

by hpgmat » Wed Nov 18, 2009 1:13 am
palvarez wrote:
hpgmat wrote:N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20
Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.

4+7n = r (3)

1 + n = r (3)

1. n +1 = 0 (mod 3)
n = 2 (mod 3)
r = n+1 (mod 3) = 3 (mod 3) = 0 Sufficient.

2. n > 20, we need to know n (mod 3). Useless.

A is sufficient.
I believe r in your equations represent the quotient ( vs R for reminder). Any how, in your first equation (4+7n = r (3))youve made an assumption that R is equal to zero. . ... how did you make that assumption? we dont know the value of R
Will Win
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 199
Joined: Sat Oct 24, 2009 4:43 pm
Thanked: 22 times
GMAT Score:710

by palvarez » Wed Nov 18, 2009 1:20 am
hpgmat wrote:
palvarez wrote:
hpgmat wrote:N IS A POSITIVE NUMBER AND R IS THE REMAINDER WHEN 4+7N IS DIVIDED BY 3. WHAT IS THE VALUE OF R?

1) N+1 IS DIVISIBLE BY 3
2)N > 20
Forget about verbal reasoning when you come to this kind of problems. Set up algebraically, using modulus, etc.

4+7n = r (3)

1 + n = r (3)

1. n +1 = 0 (mod 3)
n = 2 (mod 3)
r = n+1 (mod 3) = 3 (mod 3) = 0 Sufficient.

2. n > 20, we need to know n (mod 3). Useless.

A is sufficient.
I believe r in your equations represent the quotient ( vs R for reminder). Any how, in your first equation (4+7n = r (3))youve made an assumption that R is equal to zero. . ... how did you make that assumption?
I din't use the garbage of quotients. Just dont use quotients at all when you are dealing with remainders.

r is a remainder. Just used small letters.

"when 4 + 7n is divided by 3, remainder is r"

Translate that line, algebraically wrt modulus, etc.

4 +7n = r (modulo 3)

1 + n = r (modulo 3), because 4 (modulo 3) =1, 7n(modulo 3) = 7(modulo 3)*n(moduo 3) = 1 (modulo 3) * n (modulo 3) = n (modulo 3)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Senior | Next Rank: 100 Posts
Posts: 42
Joined: Fri Aug 15, 2008 6:14 pm
Location: India
GMAT Score:660

by aks.anupam » Wed Nov 18, 2009 2:40 am
Another simple solution can be:

1) N+1 is divisible by 3

i.e. 7N+7 would also be divisible by 3
or, 7N+7 - 3 would also be divisible by 3
or 7N+4 is also divisible by 3
This is what we need to find out: the remainder when 4+7N is divided by 3 : its zero.

Hence SUFFICIENT.

2) N>20. No other information given. Not possible to tell the remainder. Hence INSUFFICIENT.

So the answer is A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 379
Joined: Wed Jun 03, 2009 3:05 amFollowed by: 1 member
Thanked: 19 times
GMAT Score:690

by sreak1089 » Wed Nov 18, 2009 7:19 am
My Approach:

R = (7n + 4) % 3 (% is a C-programming syntax for remainder ;-)

stmt 1: n+1 divisible by 3
=> n+1 = 3k
=> n = 3k -1

Substitute n in eqn for R

R = (7(3k - 1) + 4) % 3
= (21k - 3) % 3
= 3(7k -1) % 3
= 0

Hence stmt 1 is SUFFICIENT.

stmt 2: n > 20

Multiple values possible for R.

Hence stmt 2 is NOT SUFFICIENT.

Hence Ans is A.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Newbie | Next Rank: 10 Posts
Posts: 7
Joined: Sun Jun 21, 2009 6:10 pm

by Willy » Fri Nov 20, 2009 6:50 pm
lets keep this simple...lets not get excited
....what is modulo
aks.anupam wrote:Another simple solution can be:

1) N+1 is divisible by 3

i.e. 7N+7 would also be divisible by 3
or, 7N+7 - 3 would also be divisible by 3
or 7N+4 is also divisible by 3
This is what we need to find out: the remainder when 4+7N is divided by 3 : its zero.

Hence SUFFICIENT.

2) N>20. No other information given. Not possible to tell the remainder. Hence INSUFFICIENT.

So the answer is A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Fri Aug 28, 2009 9:15 am

by geemat » Fri Nov 20, 2009 8:25 pm
Just one doubt: N is given as a positive number but not an integer. How can we assume it to be an integer?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1