yeah, just find the least common multiple. once the LCM number of hours has passed, the buses will be separated by exactly the same time interval as before - which means that an entire "cycle" of behavior has occurred. in other words, the buses' behavior is periodic, with a complete period equal to the LCM of the times.
since one of the buses leaves every ten hours and the other one leaves every fifteen hours, the LCM is only thirty hours.
this means that you only have to look at the first 30 hours. if there are no coincident departures in the first 30 hours, then there will never be any coincident departures.
if you look at the first thirty hours, then the buses will never leave at the same time. therefore, (e) is the answer.
--
by the way, pure pattern recognition (see the post by "pseudononymous") is a perfectly viable and honorable way to solve this problem. a quick glimpse at the units digits reveals, in short order, that the departures will never occur at the same time.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
