Buses leave town B at 3 pm and every 10 hours after that

[guerrero]

Buses leave town B at 3 pm and every 10 hours after that buses leave town C at 4 pm and every 15 hours after that. If the buses follow this schedule begining on Monday, what is the earliest day on which the buses leave at same time?

A) Monday
B) Tuesday
C) Thursday
D) Sunday
E) So long as they continue operating in this manner,
they will never leave at the same time.

OA
E

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Hi guerrero,

This is not something that you'd be likely to see on the GMAT. There are a couple of ways to solve it though - you COULD map out the various times and see if the two buses ever hit the same time. Here's a more elegant way though:

Since there are 24 hours in a day, we have to account for THAT repeating cycle.

3pm = 15th hour +10 hour "blocks" (we'll call these x)
4pm = 16th hour +15 hour "blocks" (we'll call these y)

It's worth noting that x and y ARE INTEGERS.

So, we have to figure out IF (notice the word IF)

15 +10x = 16 + 15y

10x - 15y = 1

x and y have to be integers, so there's NO WAY for 10x - 15y to = 1

Final Answer: E

GMAT assassins aren't born, they're made,
Rich