GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Jul 2018, 02:05

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.

Close

Request Expert Reply

Confirm Cancel

For a positive integer n, what is the remainder when n(n+1) is divided

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5836
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
For a positive integer n, what is the remainder when n(n+1) is divided [#permalink]

Show Tags

New post 03 Oct 2016, 00:50
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (01:29) correct 31% (00:55) wrong based on 110 sessions

HideShow timer Statistics

For a positive integer n, what is the remainder when n(n+1) is divided by 12?
1) n is divisible by 3.
2) n is divisible by 4.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 598
Premium Member
Re: For a positive integer n, what is the remainder when n(n+1) is divided [#permalink]

Show Tags

New post 03 Oct 2016, 01:37
MathRevolution wrote:
For a positive integer n, what is the remainder when n(n+1) is divided by 12?
1) n is divisible by 3.
2) n is divisible by 4.


12 = 4*3

We need to know if n is divisible by 4 and 3.

Stat 1: Insufficient...since we don't know about n is divisible by 4.

Stat 2: Insufficient...since we don't know about n is divisible by 3.

Both : Sufficient...n is divisible by 4 and 3...i.e n ( n+1) is divisible by 12...
Expert Post
Top Contributor
1 KUDOS received
CEO
CEO
User avatar
P
Joined: 12 Sep 2015
Posts: 2630
Location: Canada
Re: For a positive integer n, what is the remainder when n(n+1) is divided [#permalink]

Show Tags

New post 03 Oct 2016, 08:11
1
Top Contributor
1
MathRevolution wrote:
For a positive integer n, what is the remainder when n(n+1) is divided by 12?

1) n is divisible by 3.
2) n is divisible by 4.


Target question: What is the remainder when n(n+1) is divided by 12?

Statement 1: n is divisible by 3
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 3, in which case n(n+1) = 3(3+1) = 12. Here, 12 divided by 12 leaves remainder 0
Case b: n = 6, in which case n(n+1) = 6(6+1) = 42. Here, 42 divided by 12 leaves remainder 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is divisible by 4
There are several values of n that satisfy statement 2. Here are two:
Case a: n = 4, in which case n(n+1) = 4(4+1) = 20. Here, 20 divided by 12 leaves remainder 8
Case b: n = 8, in which case n(n+1) = 8(8+1) = 72. Here, 72 divided by 12 leaves remainder 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that n is divisible by 3
Statement 2 tells us that n is divisible by 4
COMBINED, we know that n is divisible by 12.
If n is divisible by 12, then we can be certain that (n)(n+1) is divisible by 12.
If (n)(n+1) is divisible by 12, then (n)(n+1) divided by 12 will leave remainder 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer =

RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Intern
Intern
avatar
B
Joined: 07 May 2016
Posts: 25
Location: India
GMAT 1: 640 Q48 V28
GMAT 2: 690 Q48 V37
GPA: 2.95
WE: General Management (Other)
Re: For a positive integer n, what is the remainder when n(n+1) is divided [#permalink]

Show Tags

New post 03 Oct 2016, 14:34
ques- For a positive integer n, what is the remainder when n(n+1) is divided by 12?
1) n is divisible by 3.
2) n is divisible by 4.

answer-

when N is divisible by 3, then N is a multiple of 3 (N can be 3,6,9,12...etc)
so this case can have both situations where N(N+1) is divisible by 12 and not divisible by 12.
For example- let N=3, thus 3*4 is divisible by 12, but if N=6 then 6*7 is not divisible by 12.
we are not certain what the remainder will be. It can either be Zero or any other number

this statement is NOT SUFFICIENT. Thus we can eliminate choices A and D. we are now left with choices B,C,E

following the same above approach for statement 2 when N is divisible by 4, we can have two situations where N(N+1) is divisible by 12 ( for N=8) but N(N+1) is not divisible by 12 (for N=4,16..etc). thus again we are not certain what will be the remainder. it can either be Zero or any other number

So this statement is also NOT SUFFICIENT. We can eliminate choice B. 2 choices are left-C,E

now if we are given N is divisible by both 3 and 4, then N is a multiple of 12. Thus, N(N+1) is divisible by 12. now we are certain about the remainder
ANswer is C
_________________

-S1D1

Expert Post
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5836
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: For a positive integer n, what is the remainder when n(n+1) is divided [#permalink]

Show Tags

New post 06 Oct 2016, 05:42
==> In the original condition, there is 1 variable (n), so D is highly likely to be the answer. In the case of 1), if =3, n(n+1)=12 with the remainder of 0,and if n=6, n(n+1)=42=12*3+6 with the remainder of 6, hence not sufficient. In the case of 2), if n=4, n(n+1)=20=12*1+8 with the remainder of 8, if n=8, n(n+1)=72=12*6 with the remainder of 0, hence not sufficient. Through 1) & 2), n=12, 24, 36… all have the remainder of 0, hence unique, and sufficient. C is the answer.
Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7247
Premium Member
Re: For a positive integer n, what is the remainder when n(n+1) is divided [#permalink]

Show Tags

New post 06 Jul 2018, 20:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: For a positive integer n, what is the remainder when n(n+1) is divided   [#permalink] 06 Jul 2018, 20:29
Display posts from previous: Sort by

For a positive integer n, what is the remainder when n(n+1) is divided

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.