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rnschmidt
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 Posted: Mon Apr 30, 2007 6:08 pm Post subject: Number Properties Question |
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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
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| Posted: Mon Apr 30, 2007 9:53 pm Post subject: Re: Number Properties Question |
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| 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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