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p(12)+11

This topic has 3 expert replies and 2 member replies
j_shreyans Legendary Member Default Avatar
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p(12)+11

Post Sat Sep 13, 2014 8:43 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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

    Answer: E

    Cheers,
    Brent

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    Last edited by Brent@GMATPrepNow on Sat Sep 13, 2014 10:50 am; edited 1 time in total

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    Post 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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    Post 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

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    Post 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 Default Avatar
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    Post 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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