BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Schedule question ?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 67
Joined: Thu Jul 17, 2014 11:04 am
Thanked: 3 times
Followed by:2 members

Schedule question ?

by sapuna » Sun Jul 20, 2014 5:58 am
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 ?
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sun Jul 20, 2014 2:47 pm
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]
Image
Top
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Sun Jul 20, 2014 10:11 pm
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
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Mon Jul 21, 2014 12:28 am
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
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Post new topic Post Reply
• Page 1 of 1