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OG What is the value of the integer P?

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG What is the value of the integer P?

Post Wed Aug 23, 2017 9:19 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    What is the value of the integer p ?

    (1) Each of the integers 2, 3, and 5 is a factor of p.
    (2) Each of the integers 2, 5, and 7 is a factor of p.

    E

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    Post Thu Aug 24, 2017 10:28 am
    AbeNeedsAnswers wrote:
    What is the value of the integer p ?

    (1) Each of the integers 2, 3, and 5 is a factor of p.
    (2) Each of the integers 2, 5, and 7 is a factor of p.

    E
    ASIDE:
    For questions involving factors (aka "divisors"), we can say:
    If k is a divisor of N, then k is "hiding" within the prime factorization of N
    Consider these examples:
    3 is a divisor of 24 because 24 = (2)(2)(2)(3), and we can clearly see the 3 hiding in the prime factorization.
    Likewise, 5 is a divisor of 70 because 70 = (2)(5)(7)
    And 8 is a divisor of 112 because 112 = (2)(2)(2)(2)(7)
    And 15 is a divisor of 630 because 630 = (2)(3)(3)(5)(7)

    Conversely, we can say that, if k is "hiding" within the prime factorization of N, then N is a multiple of k
    Examples:
    24 = (2)(2)(2)(3) <--> 24 is a multiple of 3
    (2)(5)(7) <--> 70 is a multiple of 5
    330 = (2)(3)(5)(11) <--> 330 is a multiple of 6

    ----NOW ONTO THE QUESTION-------------
    Target question: What is the value of the integer p ?

    Statement 1: Each of the integers 2, 3, and 5 is a factor of p.
    So, p = (2)(3)(5)(possibly other primes)
    This tells us that p is a multiple of 30.
    There are infinitely many values of p that satisfy statement 1.
    For example, p could equal 30 or p could equal 60 (etc)
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: Each of the integers 2, 5, and 7 is a factor of p.
    So, p = (2)(5)(7)(possibly other primes)
    This tells us that p is a multiple of 70.
    There are infinitely many values of p that satisfy statement 2.
    For example, p could equal 70 or p could equal 140 (etc)
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Statement 1 tells us that p = (2)(3)(5)(possibly other primes)
    Statement 2 tells us that p = (2)(5)(7)(possibly other primes)
    When we COMBINE the statements, we can conclude that p = (2)(3)(5)(7)(possibly other primes)
    In other words, p is a multiple of 210.
    There are infinitely many values of p that satisfy this condition.
    For example, p could equal 210 or p could equal 420 (etc)
    Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

    Answer: E

    Cheers,
    Brent

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