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 →

any shorter method to solve this

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

Re: any shorter method to solve this

by Stuart@KaplanGMAT » Tue Jun 24, 2008 7:55 pm
anjaligeorge1 wrote:How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

A. 15
B. 16
C. 17
D. 18
E. 19
There are 51 integers in the range. Since 51 is divisible by 3, the answer will be 17 (there will be an equal number of integers with remainder 0, 1 and 2).

If the number of integers hadn't been divisible by 3, then we'd have to be more careful.

For example, if the range had been 1 to 50, then the answer would be either 16 or 17 and to figure it out completely we'd look at the first 2 integers and see if one of them gave the remainder we wanted (we'd only look at the first 2, because the remaining 48 can be grouped into 16 sets of 3, so they'll be balanced).

Since 1 gives a remainder of 1 when we divide by 3, the answer for the inclusive set 1 to 50 would be 1 + 48/3 = 1 + 16 = 17.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 22
Joined: Tue Jul 03, 2007 11:23 pm
Thanked: 1 times

another way

by smashinonions » Tue Jun 24, 2008 11:12 pm
well, the range of numbers is from 0 - 50 so we have (50 -0) + 1 = 51 numbers but the last number that has a remainder of 1 when divided by 3 is 49 ( 49 / 3 = 16 with remainder 1)

now, here the numbers from 0 - 50 which leave a remainder of 1 when divided by 3 can be written as

1, 4, 7, 10, 13...

here d = 3
last term is 49

so 49 = 1 + (n - 1) * 3

(49 - 1)/ 3 = n - 1

48/ 3 = n - 1

16 = n - 1

n = 16 + 1

n = 17



i.e we have 17 numbers
------------------------------------------------------
Five years ago: GMAT - 740

Five years later: 1st Attempt - 620
GOING for 2nd attempt: Target - 740
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 170
Joined: Mon Oct 22, 2007 4:36 am
Thanked: 7 times

by erjamit » Tue Jul 29, 2008 6:29 am
But how come 1 divided by 3 will give a remainder of 1...i am bit confused by this.
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

by sudhir3127 » Tue Jul 29, 2008 6:34 am
A number can be written as = divisor* quotient + remainder

hence 1 when divided by 3 can be written as 3*0+ 1

hope its clear now...
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 170
Joined: Mon Oct 22, 2007 4:36 am
Thanked: 7 times

by erjamit » Tue Jul 29, 2008 6:36 am
I understand that....but then how do we differentiate the modulus operation from division....
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Tue Jul 29, 2008 7:34 am
erjamit wrote:I understand that....but then how do we differentiate the modulus operation from division....
That depends- what do you mean by 'modulus'? The word modulus is used in several different ways in mathematics: it can refer to absolute value (which has very little to do with division; absolute value measures distances on the number line), or it can refer to congruences in modular arithmetic (which are entirely based on properties of division), among other things.

If you are thinking of modular arithmetic (which can be helpful on the GMAT, but which you certainly don't need to know), when we say that, for example "7 is congruent to 1, mod 3" we mean "7 has the same remainder as 1 when we divide by 3". Numbers are congruent precisely because they have the same remainder, so modular arithmetic is fundamentally based on division. If anyone reading this doesn't know what I'm talking about, don't worry about it- it's not needed for the GMAT.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 170
Joined: Mon Oct 22, 2007 4:36 am
Thanked: 7 times

by erjamit » Tue Jul 29, 2008 8:59 am
Ian,

1 mod 3 is 1. (Modular arthimetic).

if 1 divided by 3 gives a remainder of 1 then what is the difference between mod and division. They are both the same then. But in computer science/mathematics they are different.

I hope you are getting my point here.

Amit
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2623
Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members
Location: Montreal
Thanked: 1090 times
GMAT Score:780

by Ian Stewart » Tue Jul 29, 2008 10:47 am
erjamit wrote:Ian,

1 mod 3 is 1. (Modular arthimetic).

if 1 divided by 3 gives a remainder of 1 then what is the difference between mod and division. They are both the same then. But in computer science/mathematics they are different.

I hope you are getting my point here.

Amit
Modular arithmetic is simply arithmetic with remainders. It is different, I suppose, from division, because when we're doing modular arithmetic, we don't care at all about quotients, only remainders. When we say "1 mod 3 is 1", that simply means "the remainder is 1 when 1 is divided by 3". When we say that "26 = 20 mod 3", that just means "26 and 20 have the same remainder when divided by 3". This can be taught in different ways- you may have learned it differently, particularly if you learned it in Computing Science- but modular arithmetic is fundamentally based on remainders. Perhaps you could explain what you think the differences are?
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 170
Joined: Mon Oct 22, 2007 4:36 am
Thanked: 7 times

by erjamit » Tue Jul 29, 2008 6:13 pm
Hi Ian,

It is getting bit confusing right now. But I don't want to spend more time on it (just 2 weeks left).

So for GMAT what I have learnt is

1/3 will leave a remainder of 1, 2/3 will leave 2 etc.

If that is the case let it be. I will just rote it.

Thanks
Amit
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

by Stuart@KaplanGMAT » Tue Jul 29, 2008 6:25 pm
erjamit wrote:Hi Ian,

It is getting bit confusing right now. But I don't want to spend more time on it (just 2 weeks left).

So for GMAT what I have learnt is

1/3 will leave a remainder of 1, 2/3 will leave 2 etc.

If that is the case let it be. I will just rote it.

Thanks
Amit
That's correct.

In fact, another way you can think of a remainder is as the numerator in a (non-reduced) mixed fraction. (Note: this only works for positive numbers, which is pretty much all you'll see on GMAT remainder questions.)

20/3 = 6 and 2/3.. so 20 divided by 3 has a remainder of 2

40/7 = 5 and 5/7... so 40 divided by 7 has a remainder of 5

3/7 = 0 and 3/7... so 3 divided by 7 has a remainder of 3
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 170
Joined: Mon Oct 22, 2007 4:36 am
Thanked: 7 times

by erjamit » Tue Jul 29, 2008 9:16 pm
WOW...thats grt...explanation.....

Thanks Stuart, however I would like to discuss more on this after my GMAT exam.

Amit
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 1022
Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members
Location: Gandhinagar
Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 11:29 pm
anjaligeorge1 wrote:How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

A. 15
B. 16
C. 17
D. 18
E. 19
shortest method possible is
if we arrange this in AP, we get 1+4+7+10+.......+49 so 1+(n-1)3=49: n=17 Ans C

Well for the case of how you can get 1 as remainder when 1 is divisble by 3. Simple funda of remainder is whatever left after dividing a number. here you try to divide one by 3. since it is not divisible quotient=0 and remainder =1
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 221
Joined: Mon Dec 22, 2008 6:24 pm
Thanked: 2 times

by mgmt_gmat » Thu Feb 11, 2010 5:03 am
50> 3k+1

from 1 to 16 multiple of 3.. hence 16 + 1(for number 1 when divided by 3 leaves remainder of 1)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 777
Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members
Location: Mumbai, India
Thanked: 117 times

by komal » Tue Feb 16, 2010 11:39 am
anjaligeorge1 wrote:How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?

A. 15
B. 16
C. 17
D. 18
E. 19
its basically 3K+1
hence series is 1,4,7,........,49
hence n=17
C. 17
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1