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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A. n (n+1) (n-4) = 7*8*3 and if n = 8 --> 8*9*4
B. n (n+2) (n-1) = 7*9*6 and if n = 8 --> 8*10*7
C. n (n+3) (n-5) = 7*10*5; eliminate as there are no multiples of 3
D. n (n+4) (n-2) = 7*11*5; eliminate as there are no multiples of 3
E. n (n+5) (n-6) = 7*12*1 and and if n = 8 --> 8*13*2

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.

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

23 Mar 2012, 21:04

IMO A.

I used an arbitrary number greater than 6 and then filled each equation out. if you happen to have chosen a number that makes more than 1 answer correct, choose a different number and check the ones that were previously correct. _________________

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

24 Mar 2012, 01:40

8

This post received KUDOS

Expert's post

18

This post was BOOKMARKED

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.

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

25 Mar 2012, 10:30

1

This post was BOOKMARKED

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.

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

15 Apr 2012, 17:12

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.

Bunuel, could you please explain how you arrive at the conclusion that "As for n-4, it will have the same remainder as (n-4)+3=n-1"? Also, is it implied that n will have a remainder of either 0 or 1, n+1 will have either 1 or 2? Thanks!

A. n (n+1) (n-4) = n (n+1) ((n-1)-3) is equivalant to (n-1) (n) (n+1)

So A is good.

Hi Bunuel, Why is n (n+1) (n-4) = n (n+1) ((n-1)-3) is equivalant to (n-1) (n) (n+1)?

Also, you said.. 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

Could you please elaborate the 2 statements above? _________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

04 May 2013, 04:36

3

This post received KUDOS

Expert's post

2

This post was BOOKMARKED

Aristocrat wrote:

Hi Bunuel,

Can you explain why the remainder should be different upon division by 3? I atill dint understood uproach

Posted from my mobile device

An integer divided by 3 can have 3 possible remainders: 0, 1, or 2.

Now, consider the product of three numbers a*b*c. If we are told that a, b, and c have different reminders upon division by three, this would mean that one of the numbers yields the remainder of zero, thus it's a multiple of 3. Thus abc is a multiple of 3.

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.

I think your solution for option A is incorrect. When you write an expression like this n (n+1) ((n-1)-3) , you are multiplying -3 with the whole expression, which eventually will turn out to (-3n+3), that is not equal to what is given. Correct me if I am wrong

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

19 Oct 2013, 03:39

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.

I took the picking numbers method but I want to understand yours as well. I understand that n (n+1), n (n+2), n (n+3)...etc will all have different remainders, and I understand the concept about the different remainders. I don't understand how you reached this statement: "As for n-4, it will have the same remainder as (n-4)+3=n-1" Can you please elaborate on that?

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

19 Oct 2013, 04:11

Expert's post

Skag55 wrote:

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.

I took the picking numbers method but I want to understand yours as well. I understand that n (n+1), n (n+2), n (n+3)...etc will all have different remainders, and I understand the concept about the different remainders. I don't understand how you reached this statement: "As for n-4, it will have the same remainder as (n-4)+3=n-1" Can you please elaborate on that?

n-1=(n-4)+3. Now, since 3 IS divisible by 3, then the remainder when (n-4)+3 is divided by by 3 is the same as n-4 is divided by 3.

For example, say n=11: The remainder when n-1=11-1=10 divided by 3 is 1. The remainder when n-4=11-4=7 divided by 3 is also 1.

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

08 Mar 2014, 00:03

I think I solved this by luck, as per below, by choosing the only answer where the sum of the digits was divisible by 3. However, testing my method by using another possible answer where the sum of the two digits is divisible by 3, shows that it is not always correct. Best to use the test method with values of n, that are not divisible by 3, in order to eliminate incorrect answer choices.

A) 1+(-4) = -3 - only answer where the sum of the two is divisible by 3. B) 2+(-1) = 1 C) 3+(-5) = -2 D) 4+(-2) = 2 E) 5+(-6)= 1

Testing another possible answer where the sum of the two ;

n(n+2)(n-5) 2+(-5)=-3 Testing with values for n that are not divisible by 3;

n=7; 7(7+2)(7-5); 7(9)(2) - has a factor divisible by 3 n=8; 8(8+2)(8-5); 8(10)(3) - has a factor divisible by 3 n=10; 10(12)(5) - has factor divisible by 3 n=11; 11(13)(6) - has factor divisible by 3

n(n-6)(n+3) -6+3=-3 n=7 ; 7(1)(10) not divisible by 3

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

25 May 2014, 09:27

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.

Why is the highlighted part important? Is that just another way of saying that at least one of the numbers in this sequence is divisible by 3. Correct?

Additionally, I see the correlation you made between n-4 and n-1(both leave a remainder of 1) but by that token, shouldn't (n+1) or (n) leave a remainder of 2 and 1 respectively? Meaning, (11+1) = 12/3 = no remainder and n (11) leaves a remainder of 2. So now we have remainders of 1,2,3 and therefore a consecutive set of integers. Is that the reason we want three different remainders?

Re: If n is an integer greater than 6, which of the following [#permalink]

Show Tags

19 Jan 2015, 01:24

Simply look for product of 3 consecutive integers....or their equivalents....i.e if a number falls under consecutive category +/- product of 3...then it work too

A )n * (n+1)* (n-4)

equivalent of (n-4)= n-1

and n-1,n,n+1 are 3 consecutive....and this prod is divisible by 3 for any integer value of n

Ans A

gmatclubot

Re: If n is an integer greater than 6, which of the following
[#permalink]
19 Jan 2015, 01:24

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...