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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

Kudos [?]: 75 [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:

41% (01:08) correct 59% (01:08) wrong based on 217 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.

Kudos [?]: 75 [0], given: 5

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 622

Kudos [?]: 771 [3], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
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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Kudos [?]: 771 [3], given: 59

Intern
Joined: 23 May 2012
Posts: 3

Kudos [?]: [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

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Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129505 [2], given: 12201

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

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23 Dec 2012, 06:38
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Expert's post
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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?

$$p(12)+11=2*3*5*7*11+11=11(2*3*5*7+1)=11*211$$. 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 [?]: 129505 [2], given: 12201

Intern
Joined: 05 Feb 2008
Posts: 40

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

Concentration: General Management, Nonprofit
GPA: 3.81
WE: Information Technology (Health Care)
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.

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

Math Expert
Joined: 02 Sep 2009
Posts: 41913

Kudos [?]: 129505 [1], given: 12201

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

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21 Aug 2013, 09:49
1
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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.
_________________

Kudos [?]: 129505 [1], given: 12201

Re: One of the questions in MGMAT test-confused with the answer   [#permalink] 21 Aug 2013, 09:49
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