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For any integer m greater than 1, $m denotes the product of

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For any integer m greater than 1, $m denotes the product of [#permalink]

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For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four
[Reveal] Spoiler: OA

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

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New post 04 Mar 2013, 10:40
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megafan wrote:
For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?

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


$ is basically a factorial of a number.

So, we are asked to find the number of primes between 7!+2 and 7!+10, inclusive.

From each number 7!+k were \(2\leq{k}\leq{10}\) we can factor out k, thus there are no pries in the given range.

For example:
7!+2=2(3*4*5*6*7+1) --> a multiple of 2, thus not a prime;
7!+3=3(2*4*5*6*7+1) --> a multiple of 3, thus not a prime;
...
7!+10=10(3*4*6*7+1) --> a multiple of 10, thus not a prime.

Answer: A.

Hope it's clear.
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Re: For any integer m greater than 1, $m denotes the product of [#permalink]

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New post 04 Mar 2013, 14:59
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Nice way to solve the problem. If you factor out the k, it should be
7!+3=3(2*4*5*6*7+1)
...
7!+10=10(3*4*6*7+1)

Quote:
For example:
7!+2=2(3*4*5*6*7+1) --> a multiple of 2, thus not a prime;
7!+2=3(2*4*5*6*7+1) --> a multiple of 3, thus not a prime;
...
7!+10=2(3*4*6*7+1) --> a multiple of 10, thus not a prime.

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

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New post 08 May 2017, 10:31
7!+2=2(3*4*5*6*7+1)=not prime;
7!+2=3(2*4*5*6*7+1)=not prime;
.........................................
7!+10=10(3*4*6*7+1) = not prime.

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

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New post 23 Oct 2017, 21:57
megafan wrote:
For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?

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


megafan its a really nice question and a real 700 level question which tests one's aptitude of quant.

I just tried to calculate the value of 7! and then tried to find number which was surely a wrong approach.

Bunuel approach and solution is awesome, which added one more trick to my quant bucket.

7!+2 = 2(7*6*...*3)
7!+3 = 3(7*6..*4*2)
7!+4 = 4(7*6*5*3*2)
..
..
7!+10 = 10(7*6*4*3)

So, there are no prime numbers between $7 + 2 and $7 + 10, inclusive..

Answer A
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Re: For any integer m greater than 1, $m denotes the product of   [#permalink] 23 Oct 2017, 21:57
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