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OG If x is a positive integer, then is x prime?

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG If x is a positive integer, then is x prime?

Post Thu Aug 24, 2017 8:38 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x is a positive integer, then is x prime?

    (1) 3x + 1 is prime
    (2) 5x + 1 is prime

    E

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    Post Fri Aug 25, 2017 12:34 am
    AbeNeedsAnswers wrote:
    If x is a positive integer, then is x prime?

    (1) 3x + 1 is prime
    (2) 5x + 1 is prime

    E
    Given: x is a positive integer
    To find out: is x prime?

    Statement 1: 3x + 1 is prime

    Since x is a positive integer, the minimum value of x = 1, thus the minimum value of 3x + 1 = 3*1 + 1 = 4, but '4' is non-prime, thus x = 1 is not a valid value.

    Let's try with x = 2, then 3x = 1 = 3*2 + 1 = 7, a prime number. So, if x = 2, then x is prime.

    We know that all the prime numbers except 2 are odd, thus, 3x + 1 = Odd.

    3x + 1 = Odd
    3x = Odd - 1 = Odd - Odd = Even
    x = Even / 3 = Even / Odd = Even (since x is a positve integer);

    Note that if an even integer is completely divisible by an odd integer, the quotient is even.

    So, we have x = Even

    If x = 2, the answer is Yes; however, if x ≠ 2, the answer is No. Insufficient.

    Statement 2: 5x + 1 is prime

    At x = 2, we see that 5x + 1 = 5*2 + 1 = 11, a prime number, so if x = 2, the answer is yes.

    As discussed in Statement 1, we know that all the prime numbers except 2 are odd, thus, 5x + 1 = Odd.

    5x + 1 = Odd
    5x = Odd - 1 = Odd - Odd = Even
    x = Even / 5 = Even / Odd = Even (since x is a positve integer);

    So, we have x = Even

    If x = 2, the answer is Yes; however, if x ≠ 2, the answer is No. Insufficient.

    Statement 1 & 2:

    x = 2, implying x is prime, and x = other even integers are applicable in both the statements, thus there is no unique answer. Insufficient.

    The correct answer: E

    Hope this helps!

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