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

 It is currently 16 Dec 2018, 18:50

### 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

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### 10 Keys to nail DS and CR questions

December 17, 2018

December 17, 2018

06:00 PM PST

07:00 PM PST

Join our live webinar and learn how to approach Data Sufficiency and Critical Reasoning problems, how to identify the best way to solve each question and what most people do wrong.
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# If n is an integer greater than 6, which of the following

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

### Hide Tags

Intern
Joined: 17 Sep 2016
Posts: 2
Re: If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

19 Sep 2016, 20:11
Bunuel wrote:
gregspirited wrote:
If n is an integer greater than 6, which of the following must be divisible by 3?

A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)

Since 3 is a prime number then in order the product to be divisible by 3 either of the multiples must be divisible by 3. Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3, meaning that one of them should have the remainder of 1, another the reminder of 2 and the third one the remainder of 0, so be divisible by 3.

For option A: n and n+1 have different remainder upon division by 3. As for n-4, it will have the same remainder as (n-4)+3=n-1, so also different than the remainders of the previous two numbers.

Hope it helps.

"Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3, meaning that one of them should have the remainder of 1, another the reminder of 2 and the third one the remainder of 0, so be divisible by 3. "

Can anyone please explain -
1. why the remainders must be different?
2. how do you know the remainders are different ?
Retired Moderator
Joined: 05 Jul 2006
Posts: 1723
If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

13 Oct 2016, 03:08
Bunuel wrote:
gregspirited wrote:
If n is an integer greater than 6, which of the following must be divisible by 3?

A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)

Since 3 is a prime number then in order the product to be divisible by 3 either of the multiples must be divisible by 3. Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3, meaning that one of them should have the remainder of 1, another the reminder of 2 and the third one the remainder of 0, so be divisible by 3.

For option A: n and n+1 have different remainder upon division by 3. As for n-4, it will have the same remainder as (n-4)+3=n-1, so also different than the remainders of the previous two numbers.

Similar question to practice: if-x-is-an-integer-then-x-x-1-x-k-must-be-evenly-divisible-126853.html

Hope it helps.

Hi Bunuel ,

how general can we make this concept ( you mentioned " since 3 is prime" so does this mean it works for all primes but not for all non primes??)
also to me the remainders idea is the same as saying ( 3 consecutive integers) am i right or am i missing something ?

would appreciate your feedback.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1723
Re: If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

13 Oct 2016, 03:48
gregspirited wrote:
If n is an integer greater than 6, which of the following must be divisible by 3?

A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)

for any to be divisible by 3 it must be the product of 3 consecutive numbers or their equivalent.

E re written in terms of equivalent is n*n*(n-1) no consecutive
d re written in terms of equivalent is n ( n+1) (n+1) non
c ...................................................... is n*n*(n+1)
b ..........................................................n * (n-1) (n-1)
a........................................................... n (n+1) (n-1) ..... answer
Manager
Joined: 20 Jan 2017
Posts: 58
Location: United States (NY)
Schools: CBS '20 (A)
GMAT 1: 750 Q48 V44
GMAT 2: 610 Q34 V41
GPA: 3.92
Re: If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

25 Jan 2017, 07:46
1) Every third integer is divisible by 3, consequently the option that contains three consecutive integers or integers that are +/-3n from the three consecutive integers, then their product will be divisible by 3.
2) The desireable combination is n(n+1)(n+2)
3) A) n(n+1)(n-4) - if we add 2*3 to the last term, we get the desired outcome - n(n+1)(n+2)

A must be divisible by 3, and it must be the correct answer.

Posted from my mobile device
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 515
Location: India
Re: If n is an integer greater than 6, which of the following must be divi  [#permalink]

### Show Tags

27 Feb 2017, 03:06
We can say that any integer can be expressed as 3a, 3a+1, 3a+2.if the expression holds true for the divisibility of 3 for all integer expression, then that will be the answer.
Option A:N = 3a, it will be 3a(3a+1)(3a-4). DIVISIBLE
N=3a+1, it will be 3a+1(3a+2)(3a-3). DIVISIBLE
N = 3a+2, it will be (3a+2)(3a+3)(3a-2). DIVISIBLE

_________________

GMAT Mentors

Intern
Joined: 05 Mar 2015
Posts: 49
Location: Azerbaijan
GMAT 1: 530 Q42 V21
GMAT 2: 600 Q42 V31
GMAT 3: 700 Q47 V38
Re: If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

31 Jul 2018, 00:27
GMAT TIGER wrote:
gregspirited wrote:
If n is an integer greater than 6, which of the following must be divisible by 3?
A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)

anything in the form of (n-1) (n) (n+1) is divvisible by 3. in other word, a product of any 3 consecutie intevers is divisible by 3.

A. n (n+1) (n-4) = n (n+1) ((n-1)-3) is equivalant to (n-1) (n) (n+1)
B. n (n+2) (n-1) is equivalant to (n+1) missing.
C. n (n+3) (n-5) is equivalant to (n-1) missing and n repeating.
D. n (n+4) (n-2) is equivalant to odd/even consqcutive integers
E. n (n+5) (n-6) is equivalant to (n+1) missing and n repeating.

So A is good.

Would you please explain why ((n-1)-3) is equivalent to (n-1)
Intern
Joined: 28 Jul 2018
Posts: 5
If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

02 Oct 2018, 09:36
GMAT TIGER wrote:
gregspirited wrote:
If n is an integer greater than 6, which of the following must be divisible by 3?
A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)

anything in the form of (n-1) (n) (n+1) is divvisible by 3. in other word, a product of any 3 consecutie intevers is divisible by 3.

A. n (n+1) (n-4) = n (n+1) ((n-1)-3) is equivalant to (n-1) (n) (n+1)
B. n (n+2) (n-1) is equivalant to (n+1) missing.
C. n (n+3) (n-5) is equivalant to (n-1) missing and n repeating.
D. n (n+4) (n-2) is equivalant to odd/even consqcutive integers
E. n (n+5) (n-6) is equivalant to (n+1) missing and n repeating.

So A is good.

can you show how A is equal to (n-1)(n)(n+1)?

edit: i see that you have n (n+1) ((n-1)-3) but I can't get from there to (n-1)(n)(n+1)
Intern
Joined: 14 Jun 2018
Posts: 8
If n is an integer greater than 6, which of the following  [#permalink]

### Show Tags

03 Nov 2018, 07:07
Bunuel would it be right to assume as follows:
Scenario 1: assume n = multiple of 3 hence all options are divisible by 3
Scenario 2: assume n not = multiple of 3 hence we look at the individual numbers being added

simply take the sum of the digits being added to n among all options and A is the only one that leaves us with a sum divisible by 3 hence A
If n is an integer greater than 6, which of the following &nbs [#permalink] 03 Nov 2018, 07:07

Go to page   Previous    1   2   3   [ 48 posts ]

Display posts from previous: Sort by

# If n is an integer greater than 6, which of the following

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

 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®.