It is currently 21 Oct 2017, 13:09

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 07 Oct 2003
Posts: 349

Kudos [?]: 21 [2], given: 0

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

Show Tags

New post 08 Jul 2004, 20:49
2
This post received
KUDOS
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

64% (02:18) correct 36% (02:11) wrong based on 552 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2013, 23:03, edited 1 time in total.
OA added.

Kudos [?]: 21 [2], given: 0

3 KUDOS received
CIO
CIO
User avatar
Joined: 09 Mar 2003
Posts: 461

Kudos [?]: 71 [3], given: 0

 [#permalink]

Show Tags

New post 08 Jul 2004, 23:52
3
This post received
KUDOS
3
This post was
BOOKMARKED
The answer is E.

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.

Kudos [?]: 71 [3], given: 0

2 KUDOS received
Director
Director
User avatar
Joined: 05 May 2004
Posts: 574

Kudos [?]: 67 [2], given: 0

Location: San Jose, CA
Re: PS Busses leaving station [#permalink]

Show Tags

New post 12 Jul 2004, 17:53
2
This post received
KUDOS
This was a tough one!
Took me 4 mins still not sure if the approach is correct :cry:

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

Hence I guess Ans is E

Anyone has a better approach to this problem?

Kudos [?]: 67 [2], given: 0

Intern
Intern
User avatar
Joined: 11 Jul 2004
Posts: 5

Kudos [?]: [0], given: 0

 [#permalink]

Show Tags

New post 12 Jul 2004, 18:54
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"

Kudos [?]: [0], given: 0

Senior Manager
Senior Manager
User avatar
Affiliations: CFA Level 2
Joined: 05 May 2004
Posts: 263

Kudos [?]: 153 [0], given: 0

Location: Hanoi
 [#permalink]

Show Tags

New post 16 Jul 2004, 20:54
1
This post was
BOOKMARKED
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"

Kudos [?]: 153 [0], given: 0

1 KUDOS received
Manager
Manager
avatar
Status: Training
Joined: 03 Jun 2013
Posts: 90

Kudos [?]: 206 [1], given: 3

Location: Canada
GPA: 3.7
GMAT ToolKit User Reviews Badge
Re: [#permalink]

Show Tags

New post 17 Jun 2013, 18:34
1
This post received
KUDOS
ian7777 wrote:
The answer is E.

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.
_________________

KUDOS please if my post was useful!

Kudos [?]: 206 [1], given: 3

Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 65

Kudos [?]: 276 [0], given: 8

GPA: 3.95
WE: Supply Chain Management (Other)
Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

New post 17 Jun 2013, 19:56
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...
_________________

Cheers!

+1 Kudos if you like my post! :-D

Kudos [?]: 276 [0], given: 8

3 KUDOS received
Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1978

Kudos [?]: 719 [3], given: 355

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

Show Tags

New post 13 Nov 2013, 07:02
3
This post received
KUDOS
1
This post was
BOOKMARKED
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).

Thus E is the correct answer

Kudos [?]: 719 [3], given: 355

Intern
Intern
avatar
Joined: 20 Jun 2011
Posts: 5

Kudos [?]: [0], given: 3

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

Show Tags

New post 27 Jul 2014, 20:37
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

Kudos [?]: [0], given: 3

Intern
Intern
avatar
Joined: 31 Oct 2015
Posts: 37

Kudos [?]: 6 [0], given: 53

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

Show Tags

New post 03 Jan 2016, 17:18
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.

Kudos [?]: 6 [0], given: 53

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17380 [2], given: 232

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

Show Tags

New post 04 Jan 2016, 05:57
2
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
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


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.

Answer (E)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17380 [2], given: 232

Manager
Manager
avatar
Joined: 09 Jul 2013
Posts: 110

Kudos [?]: 99 [0], given: 6

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

Show Tags

New post 04 Jan 2016, 11:27
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.

Answer E.
_________________

Dave de Koos
GMAT aficionado

Kudos [?]: 99 [0], given: 6

Manager
Manager
User avatar
B
Joined: 22 Jan 2014
Posts: 141

Kudos [?]: 74 [0], given: 145

WE: Project Management (Computer Hardware)
Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

New post 05 Jan 2016, 06:04
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.
_________________

Illegitimi non carborundum.

Kudos [?]: 74 [0], given: 145

Intern
Intern
avatar
Joined: 08 Mar 2016
Posts: 1

Kudos [?]: [0], given: 0

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

Show Tags

New post 12 Jun 2016, 07:37
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.

Kudos [?]: [0], given: 0

Current Student
User avatar
Joined: 03 May 2015
Posts: 262

Kudos [?]: 84 [0], given: 23

Location: South Africa
Concentration: International Business, Organizational Behavior
GPA: 3.49
WE: Web Development (Insurance)
Re: Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

Show Tags

New post 11 Jul 2016, 04:43
Mmmm this question is much easier than the discussions

B: If we put 3 PM at 0 hours,

All buses leave at intervals of 10n

C: Buses start at 4 PM : i.e; 00 hrs + 1 hr

So at C : 1 + 15t

From equation

10n = 1 + 15t

or

10n - 15t = 1

For any multiples of 10 and 15, the result will be a multiple of 5. Never 1.

E
_________________

Kudos if I helped ;)

Kudos [?]: 84 [0], given: 23

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16582

Kudos [?]: 273 [0], given: 0

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

Show Tags

New post 06 Sep 2017, 23:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Re: Buses leave town B at 3 pm and every 10 hours after that.   [#permalink] 06 Sep 2017, 23:42
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.