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manhattan math 1

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manhattan math 1

by resilient » Sun Feb 17, 2008 11:16 pm
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q
a terminating decimal?





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



i chose E but qa is B
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Re: manhattan math 1

by joshi.komal » Tue Feb 19, 2008 2:39 am
Enginpasa1 wrote:If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q
a terminating decimal?
(1) a > c
(2) b > d

i chose E but qa is B
To solve this question you should know the basics of terminating decimal.
" Any decimal, when expressed in its lowest terms, having only 2's or 5's in its denominator is a terminating decimal." After keeping this concept in mind lets solve the questions.

p/q = [2^(a-c) * 3^(b-d) ]/5^e
This fraction will be a terminating decimal only when the denominator does not contain 3. This will be true only when
b-d >0 or b> d so our rephrased question is 'Is b> d?'

Lets check the stmts.

1) a >c INSUFFICIENT eliminate answer choice A,D
2) b > d SIFFICIENT Answer is B

Hope it helps

Thanks
Komal
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