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Number properties

This topic has 1 expert reply and 0 member replies

Number properties

Post Sat Sep 16, 2017 11:32 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If p and q are positive integers, is every factor of p a factor of q?

    (1) The product of the prime factors of p is a factor of q.
    (2) p is a factor of q.

    a. statement 1 and 2 are sufficient
    b. Both are not sufficient
    c. statement 1 is sufficient while statement 2 is not sufficient
    d. statement 1 is not sufficient while statement 2 is sufficient
    e. statement 1 is sufficient

    OA is d
    why is statement not sufficient and how do you arrive at this?

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    Post Sun Sep 17, 2017 7:58 am
    Roland2rule wrote:
    If p and q are positive integers, is every factor of p a factor of q?

    (1) The product of the prime factors of p is a factor of q.
    (2) p is a factor of q.

    OA is d
    why is statement not sufficient and how do you arrive at this?
    The correct answer is B.

    Statement 1: The product of the prime factors of p is a factor of q.

    Case 1: Say p = 6 and q = 6

    Prime factors of p are 2 and 3. The product of 2 and 3 = 6 is a factor of q and all the factors of p are factors of p. The answer is Yes.

    Case 2: Say p = 12 and q = 6

    Prime factors of p are 2 and 3. The product of 2 and 3 = 6 is a factor of q, but not all factors of p are factors of q (12 is not a factor of q). The answer is No. Insufficient.

    Statement 2: p is a factor of q.

    Since p is a factor of q , q/p = integer, thus every factor of p will be a factor of q. Sufficient.

    The correct answer: B

    Hope this helps!

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