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Number Properties Question

This topic has 1 member reply
rnschmidt Newbie | Next Rank: 10 Posts Default Avatar
Joined
07 Nov 2006
Posted:
9 messages

Number Properties Question

Post Mon Apr 30, 2007 5:08 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If a, b, c, d and e are integers and p = (2^a)(3^b) and q = (2^c)(3^d)(5^e), is p/q a terminating decimal?


    (1) a > c
    (2) b > d

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    jayhawk2001 Community Manager
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    Post Mon Apr 30, 2007 8:53 pm
    rnschmidt wrote:
    If a, b, c, d and e are integers and p = (2^a)(3^b) and q = (2^c)(3^d)(5^e), is p/q a terminating decimal?


    (1) a > c
    (2) b > d
    p/q = 2^(a-c)*3(b-d) / 5^e

    The only way we can get a recurring decimal is when we have 3 in
    the denominator as 1/(3*5) is recurring.

    3 can go to the denominator when b < d

    1 - insufficient. If b > d, it is terminating. If b < d, it is non terminating

    2 - sufficient. b > d implies 3 is in the numerator and so the end
    fraction is non-terminating.

    Hence B

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