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Terminating decimals

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Terminating decimals

by ru2008 » Fri Sep 03, 2010 10:54 am
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals.
If a, b, c, d and e are non-negative 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

Source: MGMAT
OA: B

Can someone explain this?
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Source: — Data Sufficiency |
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by akdayal » Fri Sep 03, 2010 12:09 pm
1/3 is non terminating.
1/2 and 1/5 are terminating fraction,
so, b and d will decides terminating of p/q
if b > d then p/q will be terminating decimal.
if b < d then p/q will be non terminating decimal.

Hence, st 1 is not sufficient as discussed above.
st2 is sufficient

Hence B
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by Adi_Pat » Fri Sep 03, 2010 3:18 pm
Solution....

P/Q = 2^(a-c) * 3 ^(b-d) * 5^e

and a/b/c/d/e are non-negative integers....

Hence 5^e will always be an integer...i.e. terminating decimal

2^(+- integer ) is always an integer so we dont need information about whether (a-c) > = or < 0

but 3 ^ ( -ve integer ) e.g. 1/3 =0.33333 is not a terminating decimal whereas 3 ^ ( +ve integer ) e.g. 3^2=9 is.

so we need to know something about (b-d)...Hence (B)
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