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 →

Probability that n(n + 1) is a multiple of 3

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 641
Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members
Thanked: 11 times
by gmattesttaker2 » Mon Feb 17, 2014 6:11 pm
Hello,

Can you please assist with this:

If n is a positive integer between 1 and 99, inclusive, what is the probability that
n(n + 1) is a multiple of 3?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6


OA: D


I tried to solve this as follows:

n = 1 => n(n+1) = 1(1+1) - Not a multiple of 3
n = 2 => n(n+1) = 2(2+1) - Is a multiple of 3
n = 3 => 3(3+1) - Is a multiple of 3
n = 4 => 4(4+1) - Not a multiple of 3

However, I was not sure how to get the correct answer from here. Thanks for your help.

Best Regards,
Sri
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Mon Feb 17, 2014 6:24 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

If n is a positive integer between 1 and 99, inclusive, what is the probability that
n(n + 1) is a multiple of 3?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
n and (n + 1) are consecutive integers.

The product n(n + 1) will be a multiple of 3 if n is a multiple of 3 OR (n + 1) is a multiple of 3

So, P(the product is a multiple of 3) = P(n is a multiple of 3 OR n+1 is a multiple of 3)
= P(n is a multiple of 3) + P(n+1 is a multiple of 3)
= 1/3 + 1/3
= [spoiler]2/3[/spoiler]
= D

Aside: Every 3rd integer from 1 to 99 inclusive is a multiple of 3. So, P(n is a multiple of 3) = 1/3
Likewise, P(n+1 is a multiple of 3) = 1/3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Mon Feb 17, 2014 9:12 pm
Hi Sri,

Your idea to decipher the pattern behind the sequence was a good option. Sequence prompts on the GMAT will follow type of pattern; your ability to figure out that pattern might be essential to the question (such as this question) or helpful in finding an easy approach to answering whatever specific question that the prompt asks for.

You figured out the first 4 numbers in the sequence...

N=1; 1(1+1) is not a multiple of 3
N=2; 2(2+1) IS a multiple of 3
N=3; 3(3+1) iS a multiple of 3
N=4; 4(4+1) is not a multiple of 3

Now go just a little further....
N=5; 5(5+1) IS a multiple of 3
N=6; 6(6+1) IS a multiple of 3

Now we can see the sequence: NOT, IS, IS, NOT, IS, IS

So, 2 out of every 3 numbers in the sequence will give you a multiple of 3. This pattern repeats. Working up to 99, we would have 33 "sets" of NOT/IS/IS.

It will clearly be 2/3.

Final Answer: D

Keep this logic/approach in mind, especially if you don't immediately see the pattern behind a question. There's NO time to stare on Test Day; you're better served brute-forcing your way through this question and discovering the pattern than hoping that it will just "come to you."

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Mon Feb 17, 2014 10:05 pm
If n is a positive integer between 1 and 99, inclusive, what is the probability that n(n+1) is a multiple of 3?

1) 1/4
2) 1/3
3) 1/2
4) 2/3
5) 5/6
For n(n+1) to be a multiple of 3, either n or n+1 must be a multiple of 3.

n, n+1, and n+2 are 3 consecutive integers.
Of every 3 consecutive integers, exactly ONE is a multiple of 3.
Thus, P(n+2 is a multiple of 3) = 1/3.
Thus, P(either n or n+1 is a multiple of 3) = 2/3.

The correct answer is D.

Another approach is to WRITE IT OUT and LOOK FOR A PATTERN:
1*2
2*3
3*4
4*5
5*6
6*7
7*8
8*9
9*10
10*11
11*12
12*13
And so on.

The products in red show that, in 2 of every 3 cases, n(n+1) is a multiple of 3.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1