Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 09 Feb 2011
Posts: 14

If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
09 Feb 2011, 15:14
Question Stats:
74% (01:13) correct 26% (01:14) wrong based on 302 sessions
HideShow timer Statistics
If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n + 1, n + 2, n + 3, n + 4, n + 5, and n + 6? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
09 Feb 2011, 19:28
loveparis wrote: 33. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n + 1, n + 2, n + 3, n + 4, n + 5, and n + 6? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Every prime number greater than 3 is either of the form 6n  1 or of the form 6n + 1. This means that in any 6 consecutive numbers, there can be at most 2 prime numbers with a difference of 2 between them e.g. 11 (form 6n  1) and 13 (form 6n + 1). Only 2 and 3 are prime numbers that are not of one of these forms. So if you take 2, 3, 4, 5, 6, 7 as the 6 consecutive numbers, you get 4 of them prime, the maximum possible.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Manager
Joined: 22 Aug 2008
Posts: 112

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
09 Feb 2011, 18:01
for n=1, the numbers are 2,3,4,5,6,7
out if these 2,3,5,7 these 4 are prime numbers.
now for any value of n >1 all six consecutive numbers will be 3 odd and 3 even. so at max we will get 3 prime numbers(assuming all the odd numbers are prime)
so the ans is 4



Retired Moderator
Joined: 16 Nov 2010
Posts: 1253
Location: United States (IN)
Concentration: Strategy, Technology

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
10 Feb 2011, 05:24
Hi Karishma How does this follow ? "This means that in any 6 consecutive numbers, there can be at most 2 prime numbers with a difference of 2 between them" Regards, Subhash
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Director
Status: =Given to Fly=
Joined: 04 Jan 2011
Posts: 788
Location: India
Concentration: Leadership, Strategy
GMAT 1: 650 Q44 V37 GMAT 2: 710 Q48 V40 GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
10 Feb 2011, 05:44
subhashghosh wrote: Hi Karishma
How does this follow ?
"This means that in any 6 consecutive numbers, there can be at most 2 prime numbers with a difference of 2 between them"
Regards, Subhash Karishma has rightly said that primes are of the form 6n+1 or 6n1 This is not a formula for primes, it's more of a 'check' If the number can be written in the form 6n+1 or 6n1, it's PROBABLY a prime e.g. Put n=4 6x4+1=25<<< Not Prime However, 6n1=23 <<< Prime! :D See? Now assume that for a particular value of n, 6n1 and 6n+1 yield primes, in such a case the difference between the two would be: 6n+1  6n+1 = 2 Thus, the minimum difference between two prime numbers is 2. Now consider 6 consecutive numbers: n, n+1, n+2, n+3, n+4, n+5 Assume the middle term is a multiple of 6. So, n+3 and n+2 might be primes. If n+2 and n+3 are primes, then n+1 and n+5 wouldn't be primes. Thus, the maximum number of primes (greater than 3) that can occur in 6 consecutive numbers can never be more than 2! I hope the explanation is clear :D
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
10 Feb 2011, 06:35
subhashghosh wrote: Hi Karishma
How does this follow ?
"This means that in any 6 consecutive numbers, there can be at most 2 prime numbers with a difference of 2 between them"
Regards, Subhash In any 6 consecutive numbers, you can have at most 2 numbers of the form 6n  1 or 6n + 1 e.g. say the 6 consecutive numbers are: 6n  1, 6n, 6n + 1, 6n + 2, 6n + 3, 6n + 4 (e.g. 5, 6, 7, 8, 9, 10) or 6n  2, 6n  1, 6n, 6n + 1, 6n + 2, 6n + 3 (e.g. 10, 11, 12, 13, 14, 15 ) etc Remember, every number of the form 6n  1 or 6n + 1 is not prime. e.g. 25 is of the form 6n + 1 but it is not prime. But every prime greater than 3 is of the form 6n  1 or 6n + 1.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



GMAT Tutor
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 622
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
21 Sep 2015, 22:00
loveparis wrote: 33. If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n + 1, n + 2, n + 3, n + 4, n + 5, and n + 6? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6 Please tag number properties
_________________



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
27 Feb 2017, 05:03
In order to maximize the number of prime numbers in consecutive series, we have to include 2 and 3. To do this, we have to put n=0 and n=1. For n=0, the series is 1,2,3,4,5,6. Number of prime numbers are 3 For n=1, the series is 2,3,4,5,6,7. Number of prime numbers are 4 So maximum will be 4. Option D
_________________
GMAT Mentors



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
01 Mar 2017, 18:11
loveparis wrote: If n is a positive integer, what is the maximum possible number of prime numbers in the following sequences: n + 1, n + 2, n + 3, n + 4, n + 5, and n + 6?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6 In solving this problem, we must recall that 2 is the only even prime number. Thus, when n = 1, we have: 2, 3, 4, 5, 6, and 7, which gives us 4 prime numbers (2, 3, 5, and 7). Since when n is greater than 1 we will have 3 odd numbers and 3 even numbers (all greater than 2), the maximum number of prime numbers we could have is 3. Thus, by letting n = 1, we have 4 prime numbers, which is the maximum number of primes we could have. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



NonHuman User
Joined: 09 Sep 2013
Posts: 13295

Re: If n is a positive integer, what is the maximum possible num
[#permalink]
Show Tags
31 Oct 2018, 01:33
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.
_________________




Re: If n is a positive integer, what is the maximum possible num
[#permalink]
31 Oct 2018, 01:33






