mgmat 5

If we take p/q
we get, p/q=2^(a-c)*3^(b-d)*0.2^-e
or p/q=2^(a-c-e)*10^-1*3^(b-d)

1. when a>c, we dont know whether 3 will have positive or negative exponent. in case of negative it will result in non terminating decimal e.g. 2/3=0.6666666.. and so on. NS

2. when b>d it means 3 has positive exponent. even if 2 has negative exponent the result be terminating decimal.

hence b alone is suff.

Nice answer thanks. DO you recommend a way to do this with picking numbers to solidify the answer choices?

Terminating decimal rule: the only prime numbers in the denominator that can lead to terminating decimal are 2 and 5

hence, to solve this question we need to make sure that the only factors of the denominator are 2 and 5. To get to this we need to get rid of 3 in the denominator.

hence, b is sufficient.

no for some reason I lost only that in the transer. Question stands corrected at: Is 3^x<500