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Terminating Decimals

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by tlt2372 » Tue Sep 28, 2010 5:54 pm
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

OA: B

Can someone explain this answer?

Thanks!!
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by Rahul@gurome » Tue Sep 28, 2010 8:26 pm
p/q is (2^a)(3^b)/[(2^c)(3^d)(5^e)].

Now any fraction with powers of 2 or powers of 5 in the denominator is a terminating decimal because both are factors of powers of 10.
For example 3/2 = 1.5 is terminating. Here 2 is a factor of 10.
¾ = 0.75. (terminating). Here 4 = 2^2 is a factor of 100.
3/8 = 0.375. (terminating). Here 8 = 2^3 is a factor of 1000.
We can do the same thing with 5 and check.
But a fraction with 3 in the denominator is not terminating because 3 does not divide any power of 10.
So the absence of 3 in the denominator will make p/q terminating.

Let us first consider statement (1) alone.
It says a > c.
It just means that there is no 2 in the denominator. But we do not come to know whether there is a 3 in the denominator or not.
So (1) alone is not sufficient.

Next consider (2) alone.
If b > d, there is no 3 in the denominator.
We do not need to verify for 2 or 5 because there presence in the denominator does not make a decimal non-terminating.
So the given fraction p/q is terminating.
Hence statement (2) alone is sufficient to answer the question.

The correct answer is (B).
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