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

It is currently 27 Aug 2014, 11:38

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For any integer n greater than 1, n* denotes the product of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Moderator
Moderator
User avatar
Joined: 01 Sep 2010
Posts: 2375
Followers: 268

Kudos [?]: 2297 [0], given: 692

For any integer n greater than 1, n* denotes the product of [#permalink] New post 01 May 2012, 08:58
Expert's post
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:33) correct 29% (00:50) wrong based on 106 sessions
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between 6* + 2 and 6* + 6, inclusive?

A. None
B. One
C. Two
D. Three
E. Four

I'm not sure how to attack this problem. 6! come to play ......but I do not really understand how to figure out.

thanks
[Reveal] Spoiler: OA

_________________

COLLECTION OF QUESTIONS
Quant: 1. Bunuel Signature Collection - The Next Generation 2. Bunuel Signature Collection ALL-IN-ONE WITH SOLUTIONS 3. Veritas Prep Blog PDF Version
Verbal:1. Best EXTERNAL resources to tackle the GMAT Verbal Section 2. e-GMAT's ALL CR topics-Consolidated 3. New Critical Reasoning question bank by carcass 4. Meaning/Clarity SC Question Bank by Carcass_Souvik 5. e-GMAT's ALL SC topics-Consolidated-2nd Edition 6. The best reading to improve Reading Comprehension 7.Verbal question bank and Directories

1 KUDOS received
Intern
Intern
avatar
Joined: 27 Oct 2011
Posts: 13
Schools: Cambridge
Followers: 0

Kudos [?]: 9 [1] , given: 5

Re: For any integer n greater than 1......... [#permalink] New post 01 May 2012, 10:42
1
This post received
KUDOS
carcass wrote:
For any integer n greater than 1, |_ N denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between |_ 6 + 2 and |_ 6 + 6, inclusive?

(A) None
(8) One
(C) Two
(D) Three
(E) Four

I'm not sure how to attack this problem. 6! come to play ......but I do not really understand how to figure out.

thanks


There doesn't exist any prime numbers between any |_N +2 and |_N +N ,inclusive.This is bcoz |_N +x is always is divisible by
x(for x < N).

Hope that helps.
1 KUDOS received
Intern
Intern
avatar
Joined: 12 Apr 2012
Posts: 18
Followers: 1

Kudos [?]: 4 [1] , given: 0

Re: For any integer n greater than 1......... [#permalink] New post 01 May 2012, 11:05
1
This post received
KUDOS
NightFury wrote:
carcass wrote:
For any integer n greater than 1, |_ N denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between |_ 6 + 2 and |_ 6 + 6, inclusive?

(A) None
(8) One
(C) Two
(D) Three
(E) Four

I'm not sure how to attack this problem. 6! come to play ......but I do not really understand how to figure out.

thanks


There doesn't exist any prime numbers between any |_N +2 and |_N +N ,inclusive.This is bcoz |_N +x is always is divisible by
x(for x < N).

Hope that helps.


Knowing this principle obviously allows you to solve to problem pretty much immediately. However, it is possible to multiply this out in under 2 minutes. To solve for |_6, I went from high to low. 6x5=30x4=120x3=360x2=720. I wrote that out when practicing this question, but I feel like I would have saved additional time by not doing so. Once you get 720, you know you are looking for a prime number from 722, 723, 724, 725, and 726. Eliminating the evens and 725 leaves you with 723, which turns out to be divisible by 3. Answer=A.

As I said to begin though, remembering NightFury's rule speeds things up immensely.
_________________

d_n_g_

Expert Post
Moderator
Moderator
User avatar
Joined: 01 Sep 2010
Posts: 2375
Followers: 268

Kudos [?]: 2297 [0], given: 692

Re: For any integer n greater than 1......... [#permalink] New post 01 May 2012, 12:34
Expert's post
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19093
Followers: 3404

Kudos [?]: 24875 [3] , given: 2697

Re: For any integer n greater than 1, N* denotes the product of [#permalink] New post 01 May 2012, 13:27
3
This post received
KUDOS
Expert's post
carcass wrote:
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between 6* + 2 and 6* + 6, inclusive?

A. None
B. One
C. Two
D. Three
E. Four

I'm not sure how to attack this problem. 6! come to play ......but I do not really understand how to figure out.

thanks


Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.

Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.

Answer: A.

Question to practice on the same concept:
does-the-integer-k-have-a-factor-p-such-that-1-p-k-126735.html
if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 12 Jan 2012
Posts: 20
GMAT 1: 720 Q49 V39
Followers: 0

Kudos [?]: 12 [0], given: 10

Re: For any integer n greater than 1, n* denotes the product of [#permalink] New post 04 Jan 2013, 22:45
carcass wrote:
For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between 6* + 2 and 6* + 6, inclusive?

A. None
B. One
C. Two
D. Three
E. Four

I'm not sure how to attack this problem. 6! come to play ......but I do not really understand how to figure out.

thanks



Since 6! Will contain a 2 and a 5 the last digit will be a “0” so 6! = XXXX0. Now we have to check numbers XXXX2…XXXX6 => XXXX2 –> div by 2, XXXX3 ->Sum of digits div by 3 so divisible by 3,XXXX4 - >div by 2, XXXX5 -> div by 5, and XXXX6 -> div by 6.
Answer: A None
Intern
Intern
User avatar
Joined: 23 Nov 2012
Posts: 35
Location: France
Concentration: Finance, Economics
Schools: Said (D)
GMAT 1: 710 Q49 V38
WE: Sales (Investment Banking)
Followers: 0

Kudos [?]: 11 [0], given: 19

Re: For any integer n greater than 1, n* denotes the product of [#permalink] New post 05 Jan 2013, 07:48
My approach is:

6! is dividable through 1,2,3,4,5 and 6

x is dividable through y if x=z+y where z is dividable through y

for example:

12 is dividable through 4 since 12=8+4. One can also visualize this on a number line.

therefore no number between 6! and 6!+6 is a prime, which includes the intervall 6!+2 to 6!+6
_________________

Hodor?

Kudo!

Expert Post
e-GMAT Representative
User avatar
Joined: 02 Nov 2011
Posts: 1779
Followers: 1237

Kudos [?]: 3400 [0], given: 181

Re: For any integer n greater than 1, n* denotes the product of [#permalink] New post 08 Jan 2013, 02:17
Expert's post
Although all the approaches are correct. Here is one more, but less cluttered approach.

Since 6!= 720. So in nut shell, we have to find out prime # between 722 & 726. There are no prime # between 722 & 726.

-Shalabh Jain
_________________



Free Webinar: August 24, 2014 - Improve by 70 Points in 30 days: Register for this Free Webinar to learn how to define your strategy, analyze your mocks and improve by 70 points in 30 days. Click here to register.

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2188
Followers: 185

Kudos [?]: 36 [0], given: 0

Premium Member
Re: For any integer n greater than 1, n* denotes the product of [#permalink] New post 09 Mar 2014, 17:53
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: For any integer n greater than 1, n* denotes the product of   [#permalink] 09 Mar 2014, 17:53
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic For any integer n greater than 1, [n denotes the product of Bunuel 7 09 Mar 2014, 14:11
6 Experts publish their posts in the topic For any integer m greater than 1, $m denotes the product of megafan 4 04 Mar 2013, 10:31
3 Experts publish their posts in the topic For any integer n greater than 1, n* denotes the product of Galiya 6 23 Apr 2012, 10:51
for any integer k greater than 1, k* denotes the product of prospective mba 4 01 Oct 2007, 17:19
For any integer n greater than 1, n denotes the product of javed 6 25 Apr 2007, 20:53
Display posts from previous: Sort by

For any integer n greater than 1, n* denotes the product of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.