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

Expert's post

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Question Stats:

72% (01:40) correct
28% (00:58) wrong based on 146 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

5

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

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