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 350,000 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:

For any integer n greater than 1, n* denotes the product of [#permalink]
01 May 2012, 08:58

Expert's post

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

70% (01:47) correct
30% (01:18) wrong based on 196 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.

Re: For any integer n greater than 1......... [#permalink]
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).

Re: For any integer n greater than 1......... [#permalink]
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. _________________

Re: For any integer n greater than 1, N* denotes the product of [#permalink]
01 May 2012, 13:27

7

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.

Re: For any integer n greater than 1, n* denotes the product of [#permalink]
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

Re: For any integer n greater than 1, n* denotes the product of [#permalink]
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. _________________

Re: For any integer n greater than 1, n* denotes the product of [#permalink]
29 May 2015, 08:27

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. _________________

Back to hometown after a short trip to New Delhi for my visa appointment. Whoever tells you that the toughest part gets over once you get an admit is...