Terminating Decimals Are Fun!

[DMGLATT]

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

Question from MGMAT CAT #6

Answer is B

My question: Why does solving three and not two necessary?

Thanks everybody

[Captain]

If you divide anything by 2 or any power of 2 the resulting decimal always terminates.
1/2 = 0.5
1/4 = 0.25
1/8= 0.125 etc..
But if you divide by 3 the result is non terminating.
1/3 = 0.3333...
1/9 = 0.1111...
1/27 = 0.037 037 ...
etc.
you should see that any non-termminating number when divided by an integer always results in another non-terminating decimal.
Thus its necesary and sufficient just to enure that no '3' remains in the denominator. If '2' remains then result will terminate.

[DMGLATT]

thanks very much

[StaceyKoprince]

Please follow protocol: your subject should be the first 5 to 8 words of the problem. Thanks.

Captain's got it. This is also true for 5 - dividing by 5 will always lead to a terminating decimal.