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# If n is a positive integer greater than 1, then p(n) represe

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Joined: 18 Feb 2010
Posts: 22
If n is a positive integer greater than 1, then p(n) represe  [#permalink]

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Updated on: 23 Dec 2012, 06:32
2
13
00:00

Difficulty:

95% (hard)

Question Stats:

47% (01:23) correct 53% (01:15) wrong based on 285 sessions

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If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12)+11 is

A. 2
B. 11
C. 13
D. 17
E. 211

Solving
P(12)+11 = (2 x 3 x 5 x 7 x 11) +11
= 11 (2 x 3 x 5 x 7 +1)
=11(211)

Since 211 is prime, shouldn’t 11 be the 2nd smallest prime factor of the product?

Originally posted by nades09 on 22 Dec 2012, 07:24.
Last edited by Bunuel on 23 Dec 2012, 06:32, edited 1 time in total.
Renamed the topic and edited the question.
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Re: smallest prime factor of p(12)+11  [#permalink]

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22 Dec 2012, 10:51
3
2
Since 211 is prime, shouldn’t 11 be the 2nd smallest prime factor of the product?

11 is the first smallest prime factor. 211 is the second smallest prime factor
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Joined: 02 Sep 2009
Posts: 57244
Re: If n is a positive integer greater than 1, then p(n) represe  [#permalink]

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23 Dec 2012, 06:38
3
5
If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12)+11 is

A. 2
B. 11
C. 13
D. 17
E. 211

Solving
P(12)+11 = (2 x 3 x 5 x 7 x 11) +11
= 11 (2 x 3 x 5 x 7 +1)
=11(211)

Since 211 is prime, shouldn’t 11 be the 2nd smallest prime factor of the product?

$$p(12)+11=2*3*5*7*11+11=11(2*3*5*7+1)=11*211$$. Both 11 and 211 are primes: 11 is the smallest prime of p(12)+11 and 211 is the second smallest prime of p(12)+11.

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Re: If n is a positive integer greater than 1, then p(n) represe  [#permalink]

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19 Oct 2018, 10:19
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).

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Re: If n is a positive integer greater than 1, then p(n) represe   [#permalink] 19 Oct 2018, 10:19
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