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Number N is randomly selected from a set of all primes betwe

This topic has 2 expert replies and 0 member replies

Number N is randomly selected from a set of all primes betwe

Post Sun Nov 05, 2017 2:53 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+K is odd?

    (A) 1/2
    (B) 2/3
    (C) 3/4
    (D) 4/7
    (E) 5/8

    Is there a strategic approach to this question? Can any experts help?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Mon Nov 06, 2017 7:41 am
    Hello ardz24.

    First, you have to notice that N is always an odd number. Then, if you want that N+K is odd, then K has to be even (because N is odd). (it doesn't matter how we select N).

    Now, K has to be selected from {10, 15, 20, 25, 30, 35, 40}. (7 options).

    So, the favorable cases are k=10, 20, 30, 40. (4 options).

    The probability that N+K is odd is equal to:

    $$\frac{Favorable\ options}{Total\ options}=\frac{4}{7}.$$

    So, the answer should be D.

    I hope this can help you.

    I'm available if you'd like any follow up.

    Regards.

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    Post Fri Nov 10, 2017 9:50 am
    ardz24 wrote:
    Number N is randomly selected from a set of all primes between 10 and 40, inclusive. Number K is selected from a set of all multiples of 5 between 10 and 40 inclusive. What is the probability that N+K is odd?

    (A) 1/2
    (B) 2/3
    (C) 3/4
    (D) 4/7
    (E) 5/8
    Notice that there are 2 ways that the sum N+K can be ODD
    1) N is ODD and K is EVEN
    2) N is EVEN and K is ODD

    However, N cannot be EVEN, since all of the primes between 10 and 40 are ODD (11, 13, 17, 19, . . . . 31, 37)
    So, case 2 (above) is impossible

    So, P(N+K is odd) = P(N is odd AND K is even)
    = P(N is odd) x P(K is even)

    ------ASIDE-------
    Possible values of N: (11, 13, 17, 19, . . . . 31, 37)
    So, P(N is odd) = 1

    Possible values of K: (10, 15, 20, 25, 30, 35, 40)
    So, P(K is even) = 4/7
    -----------------------------------------

    So, P(N+K is odd) = P(N is odd AND K is even)
    = P(N is odd) x P(K is even)
    = 1 x 4/7
    = 4/7
    = D

    Cheers,
    Brent

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