Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

08 Jul 2004, 19:49

2

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

63% (03:18) correct
37% (02:12) wrong based on 523 sessions

HideShow timer Statistics

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.

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]

Show Tags

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]

Show Tags

13 Nov 2013, 06:02

2

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]

Show Tags

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

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

03 Jan 2016, 16:18

Just for interest. To calculate how many days it takes for the buses to leave at their original departures of 3 and 4 pm:

Bus A: Leaves at 15 and every 10 hours afterwards. After x repetitions of 10 and y days the bus leaves at 15 again and the following formula would apply:

(10 x + 15)/24 = y + 15/24 10 × = 24 y 10 * (uncommon factors of 24 with 10) = 24*(uncommon factors of 10 with 24) × = 12 y = 5

After 120 hours/5 days and 15/24ths of a day the bus will leave at 15 again.

Bus B: Leaves at 16 and every 15 hours afterwards. After x repetitions of 15 and y days the bus leaves at 16 again and the following formula would apply:

(15 x + 16)/24 = y + 16/24 15 × = 24 y 15 * (uncommon factors of 24 with 15) = 24*(uncommon factors of 15 with 24) × = 8 y = 5

After 120 hours/5 days the bus will leave at 16 again.

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

The question can be viewed as an integral solution problem. To leave at the same time on another day,

Number of hours passed after 3 pm Monday for bus leaving town B = 1 + Number of hours passed after 4 pm Monday for bus leaving town C

10B = 1+ 15C

B and C represent the number of buses that would have left since the buses that left at 3 pm Monday. Now this is just an equation in two variables where both B and C should be integers.

10B - 15C = 1 2B - 3C = 1/5

Note that the difference of two integers cannot be a fraction so this equation has no integral solutions. So the buses will never leave at the same time.

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

04 Jan 2016, 10:27

Another straightforward approach would be to just list out the time that has elapsed from the start for each bus that departs. If ever the time elapsed for two buses is the same, then the buses have departed at the same time.

To make things simpler, we can say that the first Bus B leaves at time t=0. Then the times of all Bus B departures will be 0, 10, 20, 30, etc., (always a multiple of 10). Note we don't need to deal with a 24-hour clock since all we are interested in is how many hours have passed since the beginning for each departure.

The first departure time for Bus C will be one hour after the first departure time for Bus B, so at 1 hour. All subsequent departure times for Bus C will add 15 hours onto the previous departure time: 1, 16, 31, 46, 61, etc.

We can see that the times for Bus C will never be a multiple of 10, so the buses will never depart at the same time.

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

05 Jan 2016, 05:04

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

if we look at the question then it is just asking for a number which is of the form: 10x+3 = 15y+4 or x = (5y+1)/10 no integer values exist for x. Hence, E.
_________________

Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

12 Jun 2016, 06:37

thefibonacci wrote:

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

I think the simplest approach would be to check if any term of the two series below have a common term.

A(for buses leaving at 3pm and every 10hrs after that) =3,13,23,33,43.... B(for buses leaving at 4pm and every 15 hrs after that)=4,19,34,49,64...

Thus,since there cannot be any common term in both the series,hence the buses will never leave at the same time from the two cities.

Campus visits play a crucial role in the MBA application process. It’s one thing to be passionate about one school but another to actually visit the campus, talk...

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...