p(12)+11

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Sat Sep 13, 2014 8:43 am

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

OAE

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Source: Beat The GMAT — Problem Solving | Sat Sep 13, 2014 8:43 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

p(12)+11

by Brent@GMATPrepNow » Sat Sep 13, 2014 10:12 am

j_shreyans wrote: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

OAE

By the definition, p(12) = (11)(7)(5)(3)(2)

So, p(12) + 11 = (11)(7)(5)(3)(2) + 11
= 11[(7)(5)(3)(2) + 1] I factored out the 11
= 11[210 + 1]
= 11(211)

NOTE: 11 is prime and 211 is prime

The second smallest prime factor of p(12)+11 is
p(12)+11 has only 2 prime factors: 11 and 211
So, the second smallest is 211 (the smallest is 11)

Answer: E

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 3:00 pm, edited 2 times in total.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 13, 2014 10:45 am

Brent@GMATPrepNow wrote:
The second smallest prime factor of p(12)+11 is
p(12)+11 has only 2 prime factors: 11 and 211
So, the second smallest is 11

Cheers,
Brent

Brent,

I think that you're misinterpreting the meaning of second smallest.
Of the two prime factors of p(12)+11, 11 is the smallest, so 211 is the second smallest.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 13, 2014 10:52 am

GMATGuruNY wrote:
Brent@GMATPrepNow wrote:
The second smallest prime factor of p(12)+11 is
p(12)+11 has only 2 prime factors: 11 and 211
So, the second smallest is 11

Cheers,
Brent
Brent,

I think that you're misinterpreting the meaning of second smallest.
Of the two prime factors of p(12)+11, 11 is the smallest, so 211 is the second smallest.

Good catch, Mitch.
I read it as second largest the whole time.

I have edited my response.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Sep 14, 2014 9:49 pm

j_shreyans wrote: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

OAE

P(12) = 2 x 3 x 5 x 7 x 11

Therefore, P(12)+11 = 2 x 3 x 5 x 7 x 11 + 11 = 11(2x3x5x7+1) = 11(211)

Only two primes therefore
first smallest- 11
Second smallest- 211

Answer: 211

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Wed Jul 01, 2015 9:32 pm

What a great question

I have heard the term "second smallest" in any GMAT question for the first time

first smallest -11
second smallest -211 is the answer.

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