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Buses leave town B at 3 pm and every 10 hours after that. [#permalink]
08 Jul 2004, 19:49

2

This post received KUDOS

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00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

65% (03:25) correct
35% (02:07) wrong based on 283 sessions

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

A. Tuesday B. Wednesday C. Thursday D. Sunday E. The busses will never leave at the same time

I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.

Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.

Re: PS Busses leaving station [#permalink]
12 Jul 2004, 16:53

2

This post received KUDOS

This was a tough one!
Took me 4 mins still not sure if the approach is correct

Here's my method
Let Bus B make x trips and Bus C make y trips b4 they start at the same time.
The time when they will meet is
Remainder(15+10x)/24 .... B
Remainder(16+15y)/24 .... C

These two must be equal
i.e.
Remainder(15+10x)/24=Remainder(16+15y)/24

Hence I assume we should have integer values of x,y such that
15+10x=16+15y or 10x=15y+1
no integral (x,y) combo exist for this equation

i think the giveaway is the 3pm vs 4pm start .... if they left at the same time they would eventually meet up (10hrs vs 15hrs common divisor or somesuch) but the offset means they will never meet up anytime soon, if at all. _________________

my babbling: alexmba.blogspot.com
"Everybody needs money! That's why they call it money!" -- Mickey Bergman in "Heist"

tough one for me and E.
Take a & b as the numbers of buses which leave town B & town C after the first ones. a & b must be positive integers.
We got: 3 + 10a = 4 + 15b
---> 10a = 1 + 15b
We see that: (1 + 15 x an positive integer) will never evenly divide to 10
SO E is the ans _________________

"Life is like a box of chocolates, you never know what you'r gonna get"

I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.

Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.

Hey, I don't understand this explanation:

Are you saying that the times will end in 5s? I mean, yes, the number of hours elapsed will always end in a 5 or 0, but that doesn't say much about the time, other than demonstrating that the first bus must leave, on a 24-hour clock, at times of 3, 13, 23, 9, 19, 5, 15, 1, 11, 21... and that the second bus must leave at times of 4, 19, 10, 1, 16, 7, 22..

Yes, there is a pattern that is created, but in my opinion, this is not trivial and does not follow easily from the 'number of hours elapsed ending in 5 or 0'.

Any clarification would be appreciated. As of now, I still don't know how to solve this question in a proper way. _________________

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]
17 Jun 2013, 18:56

I think this one should be E. It took me 4.44mins to manually calculate the whole thing. It turns out they never meet on the same time! This one was a tough one... _________________

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]
13 Nov 2013, 06:02

1

This post received KUDOS

lastochka wrote:

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

A. Tuesday B. Wednesday C. Thursday D. Sunday E. The busses will never leave at the same time

Buses B 3,13,23,33 etc....(pattern ending in 3 always) Buses C 4,19,34,49,54...(pattern ends only in 4 and 9).

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]
27 Jul 2014, 19:37

lastochka wrote:

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

A. Tuesday B. Wednesday C. Thursday D. Sunday E. The busses will never leave at the same time

10 and 15 are both multiple of 5 . The minimum difference between any multiple of 10 and 15 is always 0 and the next difference is 5. For example , 10 and 15 , 40 and 45. The offset of their starting time is 1 hour. We can never have account for this 1 hour difference since the difference that we can accommodate is 0 or 5. Had the departure of Bus C be (3pm + multiple of 5) then there was a possibility of buses leaving at the same time

gmatclubot

Re: Buses leave town B at 3 pm and every 10 hours after that.
[#permalink]
27 Jul 2014, 19:37

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