Problem Solving

which of the following has a terminating decimal?

10/189

5/196

16/225

25/144

39/128

The answer is easy when you have enough time. I'm posting this not to ask for the answer but to ask what or how can i solve this in 2 minutes without a calculator? there has to be a short way for doing so and I need your help on how. so please explain with detail not only the process but the way to solve it quickly, what tricks are there to solve this in 2 minutes only?

backsolving backsolving backsolving.
Notice - backsolve from E. Works for you more frequently then backsolving from A

You need to prime factorize numerator and denominator.
If denominator will consist of 2's or 5's - it is 100% terminating decimal.

E)
39/128=(13*3)/(13*2*2*2*2)==>(3/2*2*2*2) => terminating decimal.

how is 128 divisible by 13?

I understand and agree with the statement that if denominators prime factors are 2 and 5 only, then it will be terminating, however, still not seeing how you reduced the fraction.

oopsie too many silly mistakes for the day, preceding the g-day. sorry all. I am out
however! this one is still the right choice
it ll be
(13*3)/(2^6) still GOTCHA ! hehe .terminating !

(a) First convert fractions to lowest terms. (b) Then look for any denominator whose factors contain only 2 and 5.

GMAT trap: giving fractions in not-lowest terms, thereby trapping folks who know only (b).