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Number Properties Question

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rnschmidt Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
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Number Properties Question

Post Mon Apr 30, 2007 5:08 pm
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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