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

It is currently 25 Jun 2018, 01:02

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the remainder, when n(n+2) is divided by 24 for a positive int

  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
D
Joined: 16 Aug 2015
Posts: 5610
GMAT 1: 800 Q59 V59
GPA: 3.82
What is the remainder, when n(n+2) is divided by 24 for a positive int [#permalink]

Show Tags

New post 14 Aug 2017, 01:28
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (01:14) correct 32% (01:37) wrong based on 60 sessions

HideShow timer Statistics

What is the remainder, when n(n+2) is divided by 24 for a positive integer x?

1) n is an even integer
2) n has remainder 0 or 1 when it is divided by 3.

_________________

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"

2 KUDOS received
Manager
Manager
avatar
G
Joined: 15 Feb 2017
Posts: 80
Re: What is the remainder, when n(n+2) is divided by 24 for a positive int [#permalink]

Show Tags

New post 14 Aug 2017, 01:40
2
n is an even integer and n leaves 0 or 1 when divided by3.
When n is 10 it leaves a remainder 1 when divided by 3.n(n+2)=10*12=120. 120 when divided by 24 leaves no remainder.
Next case n=12 which is evenly divided by 3. 12*14 =168. 168 when divided by 24 leaves 0 as remainder
Take other cases n=18,22. In all cases n(n+2) is perfectly divided by 24.So the answer is C Both statements are sufficient.
Please Give me kudos . I need them badly
Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5610
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: What is the remainder, when n(n+2) is divided by 24 for a positive int [#permalink]

Show Tags

New post 16 Aug 2017, 02:39
Condition 1)
There are two kinds of even integers, which are n = 4k or n = 4k + 2 for some integer k. That means n could have 0 or 2 as a remainder when it is divided by n. If n = 4k, n(n+2) = 4k(4k+2) = 8k(2k+1) and n(n+1) is a multiple of 8. If n= 4k+2, n(n+2) = (4k+2)(4k+2+2) = 2(2k+1)*4(k+1) = 8(2k+1)(k+1) and n(n+1) is a multiple of 8. For both cases, n(n+1) is a multiple of 8. However, we can’t identify the remainder when it is divided by 3 from the condition 1).

Condition 2)
n = 3k or n = 3k +1. If n = 3k, n(n+2) = 3k(3k+2) is a multiple of 3. If n = 3k + 1, n(n+2) = (3k+1)(3k+3) = 3(3k+1)(k+1) is a multiple of 3. Thus, for both cases, n(n+1) is a multiple of 3. However, we can’t identify the remainder when it is divided by 8 from the condition 2).

Condition 1) & 2)
From the condition 1), n(n+1) is a multiple of 8. And n(n+1) is a multiple of 3 from the condition 2). Therefore, n(n+1) is a multiple of 24 from the both conditions 1) & 2) together.

Ans: 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"

Manager
Manager
avatar
G
Joined: 26 Jun 2017
Posts: 243
Location: Russian Federation
Concentration: General Management, Strategy
WE: Information Technology (Other)
Re: What is the remainder, when n(n+2) is divided by 24 for a positive int [#permalink]

Show Tags

New post 16 Aug 2017, 16:16
1
MathRevolution wrote:
What is the remainder, when n(n+2) is divided by 24 for a positive integer x?

1) n is an even integer
2) n has remainder 0 or 1 when it is divided by 3.


1) n = 2k
2k(2k+2)=4k(k+1)
If k = 1, the remainder is 8, if k = 2, the remainder is 0 ---> A is not the answer.

2) n = 3p or n=3m+1
3p(3p+1) or (3m+1)(3m+3)=3(3m+1)(m+1)
If p = 1, the remainder is 12, if p = 2, ther remainder is 18 ---> B is not the answer.

Lets combine them. 1)+2)
n(n+2)=4k(k+1)=3p(3p+1)
or
n(n+2)=4k(k+1)=3(3m+1)(m+1)
From (1) we have n(n+2) is divisible by 8 (because k and k+1 are 2 consecutive numbers, so one of them is even)
From (2) we have n(n+2) is divisible by 3 (both cases)
----->n(n+2) is divisible by 24, the raminder is always equal to 0.
Re: What is the remainder, when n(n+2) is divided by 24 for a positive int   [#permalink] 16 Aug 2017, 16:16
Display posts from previous: Sort by

What is the remainder, when n(n+2) is divided by 24 for a positive int

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


cron

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®.