Schedule question ?

Question

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

1) Tuesday

2) Wednesday

3) Thursday

4) Sunday

5) Never - correct. I tried calculating all the day until Sunday but it was way too much work. Also , the buses don`t leave at completely seperate hours ( for example at even and uneven hours ) , so how do we prove this ?

Rich.C@EMPOWERgmat.com · Answer

Hi sapuna,

This question is based primarily on pattern-matching, although you can "brute force" it in the way that you did and prove that the buses don't ever leave at the same time. Here's how the pattern-matching approach can save you a lot of effort:

Buses leave B at 3pm and every 10 hours thereafter….
Buses leave C at 4pm and every 15 hours thereafter…

3pm is the 15th hour of the day. 4pm is the 16th hour of the day. We're looking to see if the start times EVER occur at the same time.

B: 15, 25, 35, 45, 55, etc.

Notice how EVERY starting hour "ends in a 5"

C: 16, 31, 46, 61, 76, 91, etc.

Notice how EVERY starting hour EITHER "ends in a 6 or a 1"

This means that the two busses will NEVER leave at the same time.

Final Answer: E

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

Contact Rich at [email protected]

GMATinsight · Answer

sapuna wrote:Buses leave town B at 3 p.m. and 10 hours after that. Buses leave town C at 4 p.m. and 15 hours after that. If the buses follow this schedule , starting on Monday, what is the earliest day on which the buses leave at the same time ?

1) Tuesday

2) Wednesday

3) Thursday

4) Sunday

5) Never - correct. I tried calculating all the day until Sunday but it was way too much work. Also , the buses don`t leave at completely seperate hours ( for example at even and uneven hours ) , so how do we prove this ?

I would say it's not a bad idea to solve this manually...

Bus leaving B leaves after 10 hours (3 PM onwards)
3 PM, 1 AM, 11 AM, 9 PM, 7 AM, 5 PM, 3 PM (Cycle repeats)

Bus leaving C leaves after 15 hours (4 PM onwards)
4 PM, 7 PM, 10 AM, 1 PM, 4 AM, 7 PM (Cycle repeats)

NO TIME IS COMMON BETWEEN TWO CALCULATION AND THE TIMINGS HAVE STARTED REPEATING IN EACH OF THE CYCLE

THEREFORE BUSES NEVER LEAVE SAME TIME

Answer: Option E

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GMATinsight · Answer

Here is another WOW Method

First bus leaves after every 10 Hours
Second bus leaves after every 15 Hours

Since the first Bus leaves at 3PM and another leaves at 4 PM then the difference between them is 1 Hour

If the Xth bus leaving B meets Yth bus from C then it meets after 10X hours
Similarly the Yth bus leaving C meets any bus from B then it meets after 15Y-1 hours

For them to meet

10X = 15Y-1 Which has no Integer solution therefore They never meet

Answer: Option E

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