Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 Aug 2016, 06:30

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6838
Location: Pune, India
Followers: 1928

Kudos [?]: 11975 [0], given: 221

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

### Show Tags

09 Jul 2013, 01:16
VeritasPrepKarishma wrote:

In my opinion, using logic is almost always better than plugging in. Plugging in is full of possibilities of making mistakes - incorrect calculation, not considering all possibilities, getting lost in the options etc.

Logic is far cleaner.

I know that talking about positive integers, in any set of 3 consecutive positive integers, one integer will be divisible by 3 and the other 2 will not be.

So I am looking for 3 consecutive positive integers e.g. (n-1)n(n+1)

Note that (n-4) is equivalent to (n-1) since if (n-4) is divisible by 3, so is (n-1). If (n-4) is not divisible by 3, neither is (n-1) (because the difference between these two integers is 3)
Hence (A) is equivalent to 3 consecutive integers.

On same lines, note that n is equivalent to (n-3), (n + 3), (n + 6) etc.

Responding to a pm:

As said here, I prefer to use logic rather than number plugging. Number plugging is usually the last resort. Given above is the logical solution to this problem. For more on this topic, check:

http://www.veritasprep.com/blog/2011/09 ... c-or-math/
http://www.veritasprep.com/blog/2011/09 ... h-part-ii/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 21 Jun 2011 Posts: 84 Location: United States Concentration: Accounting, Finance WE: Accounting (Accounting) Followers: 1 Kudos [?]: 31 [0], given: 13 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 09 Jul 2013, 06:42 VeritasPrepKarishma wrote: VeritasPrepKarishma wrote: In my opinion, using logic is almost always better than plugging in. Plugging in is full of possibilities of making mistakes - incorrect calculation, not considering all possibilities, getting lost in the options etc. Logic is far cleaner. I know that talking about positive integers, in any set of 3 consecutive positive integers, one integer will be divisible by 3 and the other 2 will not be. So I am looking for 3 consecutive positive integers e.g. (n-1)n(n+1) Note that (n-4) is equivalent to (n-1) since if (n-4) is divisible by 3, so is (n-1). If (n-4) is not divisible by 3, neither is (n-1) (because the difference between these two integers is 3) Hence (A) is equivalent to 3 consecutive integers. Answer (A) On same lines, note that n is equivalent to (n-3), (n + 3), (n + 6) etc. Responding to a pm: As said here, I prefer to use logic rather than number plugging. Number plugging is usually the last resort. Given above is the logical solution to this problem. For more on this topic, check: http://www.veritasprep.com/blog/2011/09 ... c-or-math/ http://www.veritasprep.com/blog/2011/09 ... h-part-ii/ Thanks. Even I was looking forward to logic to save some time on the real exam Intern Joined: 06 Jun 2013 Posts: 1 GPA: 3 WE: Consulting (Consulting) Followers: 0 Kudos [?]: 0 [0], given: 0 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 09 Jul 2013, 10:37 I wish someone would solve this question step by step. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6838 Location: Pune, India Followers: 1928 Kudos [?]: 11975 [0], given: 221 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 09 Jul 2013, 21:34 JaJaIrie wrote: I wish someone would solve this question step by step. That's the point - there are no steps here. There is no process you have to follow. You just need to understand the logic and you will have your answer. Check Bunuel's explanation here: if-n-is-an-integer-greater-than-6-which-of-the-following-mu-139279.html#p1123734 and my explanation here: if-n-is-an-integer-greater-than-6-which-of-the-following-mu-139279.html#p1242663 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 29 May 2013
Posts: 6
Followers: 0

Kudos [?]: 15 [0], given: 6

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

### Show Tags

08 Oct 2013, 05:00
Dear Bunuel,

"Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3"

Why is this? Why the numbers must have different reminders?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6838
Location: Pune, India
Followers: 1928

Kudos [?]: 11975 [1] , given: 221

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

### Show Tags

08 Oct 2013, 21:25
1
KUDOS
Expert's post
khairilthegreat wrote:
Dear Bunuel,

"Now, to guarantee that at least one multiple is divisible by 3, these numbers must have different remainders upon division by 3"

Why is this? Why the numbers must have different reminders?

Any positive number will take one of three forms: 3m, (3m+1) or (3m+2) i.e. either it will be divisible by 3, will leave remainder 1 or will leave remainder 2 when divided by 3. If the number takes the form 3m, the number after it is of the form 3m+1 and the one after it is of the form 3m+2.

If we have 3 consecutive numbers such as a, (a+1), (a+2), we know for sure that at least one of them is divisible by 3 since one of them will be of the form 3m. We don't know which one but one of them will be divisible by 3.

So given numbers such as (n-1)*n*(n+1), we know that the product is divisible by 3.
In the given options, we don't know whether n is divisible by 3 or not. We need to look for the option which has 3 consecutive numbers i.e. in which the terms leave a remainder of 0, 1 and 2 to be able to say that the product will be divisible by 3.

Note a product such as n(n+3)(n+6). When this is divided by 3, we cannot say whether it is divisible or not because all three factors will leave the same remainder, 1.
Say n = 4. Product 4*7*10. All these factors are of the form 3m+1. We don't have any 3m factor here.
So we need the factors to have 3 different remainders so that one of them is of the form 3m.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 29 May 2013 Posts: 6 Followers: 0 Kudos [?]: 15 [0], given: 6 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 09 Oct 2013, 03:17 Thanks Karishma, It is clear now. Manager Joined: 07 Apr 2012 Posts: 126 Location: United States Concentration: Entrepreneurship, Operations Schools: ISB '15 GMAT 1: 590 Q48 V23 GPA: 3.9 WE: Operations (Manufacturing) Followers: 0 Kudos [?]: 10 [0], given: 45 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 09 Oct 2013, 05:45 (n-4)+3=n-1 How to conclude on this ? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6838 Location: Pune, India Followers: 1928 Kudos [?]: 11975 [0], given: 221 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 09 Oct 2013, 21:43 ygdrasil24 wrote: (n-4)+3=n-1 How to conclude on this ? When talking about 'divisibility by 3', (n - 4) and (n - 1) are of the same form. This means that if (n-1) is divisible by 3, so is (n - 4). If (n-1) leaves a remainder of 1 when divided by 3, so does (n-4). If (n-1) leaves a remainder of 2 when divided by 3, so does (n-4). the reason for this is that (n-1) and (n-4) have a difference of 3 between them. If (n-4) = 5, (n-1) = 8. Both leave remainder 2 when divided by 3 If (n-4) = 6, (n-1) = 9. Both leave remainder 0 when divided by 3 If (n-4) = 7, (n-1) = 10. Both leave remainder 1 when divided by 3 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Joined: 07 Apr 2012
Posts: 126
Location: United States
Concentration: Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 590 Q48 V23
GPA: 3.9
WE: Operations (Manufacturing)
Followers: 0

Kudos [?]: 10 [0], given: 45

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

### Show Tags

10 Oct 2013, 01:44
VeritasPrepKarishma wrote:
ygdrasil24 wrote:
(n-4)+3=n-1

How to conclude on this ?

When talking about 'divisibility by 3', (n - 4) and (n - 1) are of the same form. This means that if (n-1) is divisible by 3, so is (n - 4). If (n-1) leaves a remainder of 1 when divided by 3, so does (n-4). If (n-1) leaves a remainder of 2 when divided by 3, so does (n-4). the reason for this is that (n-1) and (n-4) have a difference of 3 between them.

If (n-4) = 5, (n-1) = 8. Both leave remainder 2 when divided by 3
If (n-4) = 6, (n-1) = 9. Both leave remainder 0 when divided by 3
If (n-4) = 7, (n-1) = 10. Both leave remainder 1 when divided by 3

Okay. Thanks. Its a bit awkward to get the logic initially. usually when asked for division by 3, i would look for a 3N type number. If the question had , say, to check for 4, then in that case we should be having 4 multipliers of n something like N(N-2)(N+3)(N-4) and so on ? So that we can have remainders as 0,1,2,3
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 6838
Location: Pune, India
Followers: 1928

Kudos [?]: 11975 [0], given: 221

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

### Show Tags

10 Oct 2013, 04:35
ygdrasil24 wrote:
VeritasPrepKarishma wrote:
ygdrasil24 wrote:
(n-4)+3=n-1

How to conclude on this ?

When talking about 'divisibility by 3', (n - 4) and (n - 1) are of the same form. This means that if (n-1) is divisible by 3, so is (n - 4). If (n-1) leaves a remainder of 1 when divided by 3, so does (n-4). If (n-1) leaves a remainder of 2 when divided by 3, so does (n-4). the reason for this is that (n-1) and (n-4) have a difference of 3 between them.

If (n-4) = 5, (n-1) = 8. Both leave remainder 2 when divided by 3
If (n-4) = 6, (n-1) = 9. Both leave remainder 0 when divided by 3
If (n-4) = 7, (n-1) = 10. Both leave remainder 1 when divided by 3

Okay. Thanks. Its a bit awkward to get the logic initially. usually when asked for division by 3, i would look for a 3N type number. If the question had , say, to check for 4, then in that case we should be having 4 multipliers of n something like N(N-2)(N+3)(N-4) and so on ? So that we can have remainders as 0,1,2,3

When considering division by 4, N and N-4 are the same thing.
We would be looking for a product such as N(N+1)(N+2)(N+3) or (N-1)N(N+1)(N-2) (since N-1 is the same as N+3 and N-2 is the same as N+2 so this product is same as the first product) etc
Check out:
http://www.veritasprep.com/blog/2011/09 ... c-or-math/
http://www.veritasprep.com/blog/2011/09 ... h-part-ii/

The logic is explained in detail in these 2 posts.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 07 Apr 2012 Posts: 126 Location: United States Concentration: Entrepreneurship, Operations Schools: ISB '15 GMAT 1: 590 Q48 V23 GPA: 3.9 WE: Operations (Manufacturing) Followers: 0 Kudos [?]: 10 [0], given: 45 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 10 Oct 2013, 05:33 OK Thanks , Can I subscribe to get updates from your blog? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6838 Location: Pune, India Followers: 1928 Kudos [?]: 11975 [1] , given: 221 Re: If n is an integer greater than 6, which of the following mu [#permalink] ### Show Tags 10 Oct 2013, 21:46 1 This post received KUDOS Expert's post ygdrasil24 wrote: OK Thanks , Can I subscribe to get updates from your blog? Sure. You can subscribe to our blog through Twitter/Facebook/Email/News Readers http://www.veritasprep.com/blog/ Check out these options in the 'Connect With Veritas Prep' box on this page _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 04 Aug 2013
Posts: 6
Concentration: Sustainability, Entrepreneurship
WE: Architecture (Energy and Utilities)
Followers: 0

Kudos [?]: 4 [0], given: 8

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

### Show Tags

29 Oct 2013, 16:50
Try with 1, and that will limit us to option A & D.
Alternatively, looking at all the options, only A will result to 3. This is how I did
1. N+1 + N -4 = 2n-3 (Any no. will give a multiple of 3).
2. N-1 + N+2 = 2n+1
3. N-5 + N+3 = 2n-2
4. N-2 + N+4 = 2n +2
5. N-6 + N+5 = 2n -1

*not sure if this is correct method.
Intern
Joined: 28 Sep 2013
Posts: 1
Schools: AGSM '16
Followers: 0

Kudos [?]: 0 [0], given: 1

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

### Show Tags

30 Oct 2013, 18:50
multiplication of three consecutive numbers is always divisible by 3,
i.e (n-1)*n*(n+1) or n*(n+1)*(n+2) or (n-2)*(n-1)*n
check the option that represents any of the above types.

a) satisfies (n-1)*n*(n+1) condition (n-4)= (n-1) because difference of both is 3
for verification substitute n=13, 14, 19, 10
Intern
Joined: 02 Jan 2014
Posts: 12
Followers: 0

Kudos [?]: 13 [0], given: 15

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

### Show Tags

09 Mar 2014, 11:00
Multiple brilliant answers in this wonderful forum... as always. However... I found a way that I -personally- understood better, and a way I think I can use in a time-constrained manner in the actual exams.

According to GMAT materials, the ways where an integer can be divided by 3 are
1) when the sum of the integer DIGITS is divisible by 3
2) the integer have multiple of 3's
3) a consecutive set of 3 integers can be divisible by both 2 and 3 (factor foundation rule)

There are two ways to solve this
1) Plugging in: Undoubtedly, plugging in numbers to the 5 options below is perhaps the simplest and easiest way to answer this question. To save time on computation, using the sum of integer DIGITS may accelerate your process, or looking for multiples of 3s. For example:
Option A: n(n + 1)(n - 4) = 7(7 +1)(7 - 4) = (7)(8)(3)

2) Look for patterns
Given the answer options, which are adjusting the position of n on the number lines, another way is to scan if any of these answer choices provide clues to consecutive numbers.

In Option (A): we have a partial consecutive set of N, N+1. It looks like it is missing a N+2 or N-1. OR is it?
Now look closer at (N-4). From a consecutive set perspective, (N-4) is also the same "position" as (N-1)
Therefore this answer choice has N, N+1 and N-1. This is a consecutive set that is both divisible by 2 and 3.

All other options will not have such a relationship:
Option (B) n(n + 2)(n – 1):
We have N, N+2, and (N-1 or N+3....). Therefore missing N+1 to make a consecutive set

Option (C) n(n + 3)(n – 5)
We have N, N+3, and (N-5 or N-2 or N+1....) Therefore missing N+2 to make a consecutive set

Option (D) n(n + 4)(n – 2)
We have N, N+4 and (N-2, N+1, N+4...). Therefore missing N+2 to make a consecutive set

Option (E) n(n + 5)(n – 6)
We have N, N+5 and (N-6, N-3, N, N+3....). Therefore missing N+2 to make a consecutive set
Intern
Joined: 02 Jan 2014
Posts: 12
Followers: 0

Kudos [?]: 13 [0], given: 15

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

### Show Tags

09 Mar 2014, 11:02
Multiple brilliant answers in this wonderful forum... as always. However... I found a way that I -personally- understood better, and a way I think I can use in a time-constrained manner in the actual exams.

Concept
According to GMAT materials, the ways where an integer can be divided by 3 are
1) when the sum of the integer DIGITS is divisible by 3
2) the integer have multiple of 3's
3) a consecutive set of 3 integers can be divisible by both 2 and 3 (factor foundation rule)

There are two ways to solve this
1) Plugging in: Undoubtedly, plugging in numbers to the 5 options below is perhaps the simplest and easiest way to answer this question. To save time on computation, using the sum of integer DIGITS may accelerate your process, or looking for multiples of 3s. For example:
Option A: n(n + 1)(n - 4) = 7(7 +1)(7 - 4) = (7)(8)(3)

2) Look for patterns
Given the answer options, which are adjusting the position of n on the number lines, another way is to scan if any of these answer choices provide clues to consecutive numbers.

In Option (A): we have a partial consecutive set of N, N+1. It looks like it is missing a N+2 or N-1. OR is it?
Now look closer at (N-4). From a consecutive set perspective, (N-4) is also the same "position" as (N-1)
Therefore this answer choice has N, N+1 and N-1. This is a consecutive set that is both divisible by 2 and 3.

All other options will not have such a relationship:
Option (B): n(n + 2)(n – 1):
We have N, N+2, and (N-1 or N+3....). Therefore missing N+1 to make a consecutive set

Option (C): n(n + 3)(n – 5)
We have N, N+3, and (N-5 or N-2 or N+1....) Therefore missing N+2 to make a consecutive set

Option (D): n(n + 4)(n – 2)
We have N, N+4 and (N-2, N+1, N+4...). Therefore missing N+2 to make a consecutive set

Option (E): n(n + 5)(n – 6)
We have N, N+5 and (N-6, N-3, N, N+3....). Therefore missing N+2 to make a consecutive set
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11125
Followers: 511

Kudos [?]: 134 [0], given: 0

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

### Show Tags

20 Mar 2015, 11:22
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.
_________________
Senior Manager
Joined: 29 Oct 2013
Posts: 297
Concentration: Finance
GMAT 1: 750 Q V46
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 13

Kudos [?]: 330 [0], given: 197

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

### Show Tags

01 Dec 2015, 03:28
EMPOWERgmatRichC: can you also provide some insights into this question? What principle is GMAT testing here? What's the most efficient way to tackle it etc. Thanks
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7199
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 314

Kudos [?]: 2132 [1] , given: 161

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

### Show Tags

01 Dec 2015, 21:43
1
KUDOS
Expert's post
Hi MensaNumber,

This question can be solved rather easily by TESTing VALUES, although the work itself will take a bit longer than average and it would help a great deal if you could spot the subtle Number Properties involved.

From the question stem, you can see that we're dealing with division by 3 (or the 'rule of 3', if you learned the concept that way). You don't actually have to multiply out any of the answer choices though - you just need to find the one answer that will ALWAYS have a '3' in one of its 'pieces.' The subtle Number Property I referred to at the beginning is the 'spacing out' of the terms.

(1)(2)(3) is a multiple of 3, since it's 3 times some other integers.

(5)(6)(7) is also a multiple of 3, since we can find a 3 'inside' the 6, so we have 3x2 times some other integers.

Looking at the answer choices to this question, we're clearly NOT dealing with consecutive integers, but the 'cycle' of integers is something that we can still take advantage of.

For example, we know that...
When n is an integer, (n+1)(n+2)(n+3) will include a multiple of 3, since it's 3 consecutive integers (one of those 3 terms MUST be a multiple of 3, even if you don't know exactly which one it is).

You can take this same concept and 'move around' any (or all) of the pieces:

(n+1)(n+2)(n+6) will also include a multiple of 3 (that third term is 3 'more' than 'n+3').

Instead of adding a multiple of 3 to a term, you could also subtract a multiple of 3 from a term.

eg. (n-2)(n+2)(n+3) will also include a multiple of 3 (that first timer is 3 'less' than 'n+1').

The correct answer to this question subtracts a multiple of 3 from one of the terms.

[Reveal] Spoiler:
A

All things being equal, I'd still stick to TESTing VALUES (and not approaching the prompt with math theory) - the math is easy and you can put it 'on the pad' with very little effort.

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If n is an integer greater than 6, which of the following mu   [#permalink] 01 Dec 2015, 21:43

Go to page   Previous    1   2   3    Next  [ 41 posts ]

Similar topics Replies Last post
Similar
Topics:
2 If n is an integer greater than 7, which of the following must be divi 4 02 Jun 2016, 04:44
1 if n is a positive integer greater than 8, which of the following must 7 13 Mar 2016, 06:49
2 If n is an integer greater than 6, which of the folowing mus 1 11 Aug 2013, 01:08
12 If n is an integer greater than 6, which of the following must be divi 18 13 Sep 2010, 11:02
52 If n is an integer greater than 6, which of the following 28 26 Nov 2007, 14:15
Display posts from previous: Sort by