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

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Intern
Joined: 18 Feb 2010
Posts: 28
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Kudos [?]: 66 [0], given: 5

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

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22 Dec 2012, 07:24
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Difficulty:

95% (hard)

Question Stats:

42% (02:11) correct 58% (01:06) wrong based on 185 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

[Reveal] Spoiler:
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?
[Reveal] Spoiler: OA

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
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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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Intern
Joined: 23 May 2012
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Kudos [?]: 0 [0], given: 19

Re: smallest prime factor of p(12)+11 [#permalink]

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23 Dec 2012, 03:59
p(12)=11*211,shouldnt 11 be the smallest prime
Math Expert
Joined: 02 Sep 2009
Posts: 38989
Followers: 7748

Kudos [?]: 106455 [2] , given: 11626

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

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23 Dec 2012, 06:38
2
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Expert's post
2
This post was
BOOKMARKED
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

[Reveal] Spoiler:
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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Kudos [?]: 15 [0], given: 12

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

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21 Aug 2013, 09:45
Hi

I just took a test in free GMAT test section (MGMAT test)

There is one question which says

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

The OA is
[Reveal] Spoiler:
E.

But i am not convinced by the explanation.

Math Expert
Joined: 02 Sep 2009
Posts: 38989
Followers: 7748

Kudos [?]: 106455 [1] , given: 11626

Re: One of the questions in MGMAT test-confused with the answer [#permalink]

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21 Aug 2013, 09:49
1
KUDOS
Expert's post
willisback wrote:
Hi

I just took a test in free GMAT test section (MGMAT test)

There is one question which says

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

The OA is E. But i am not convinced by the explanation.

Merging similar topics. Please refer to the solutions above.

P.S. Please hide OA under the spoiler. Thank you.
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Re: One of the questions in MGMAT test-confused with the answer   [#permalink] 21 Aug 2013, 09:49
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