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:
A man cycling along the road noticed that every 12 minutes [#permalink]
04 Jan 2010, 03:44
4
This post received KUDOS
40
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
95% (hard)
Question Stats:
36% (03:14) correct
64% (01:58) wrong based on 622 sessions
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
A. 5 minutes B. 6 minutes C. 8 minutes D. 9 minutes E. 10 minutes
I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test? Thank you in advance!!
Re: test m08 question n18 [#permalink]
04 Jan 2010, 03:57
26
This post received KUDOS
Expert's post
18
This post was BOOKMARKED
lucalelli88 wrote:
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
I didn't get how to solve this problem. Can someone explain me more detailed than solution provided by the test? Thank you in advance!!
A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses? A. 5 minutes B. 6 minutes C. 8 minutes D. 9 minutes E. 10 minutes
Let's say the distance between the buses is \(d\). We want to determine \(Interval=\frac{d}{b}\), where \(b\) is the speed of bus.
Let the speed of cyclist be \(c\).
Every 12 minutes a bus overtakes cyclist: \(\frac{d}{b-c}=12\), \(d=12b-12c\);
Every 4 minutes cyclist meets an oncoming bus: \(\frac{d}{b+c}=4\), \(d=4b+4c\);
I might be VERY wrong..But when i don't get the answers..I go off track..So I'm not sure that this is the answer.. But marking the answer with some guess is better than NO guess.!!
Let say the road is a straight line AB. The cyclist starts frm A and Bus starts frm B.
So in 4 min, let the distance traveled by Cyc is x, so distance traveled by Bus is (AB - x) so 4 = x/c...........................1 and 4= (AB - x)/b..................................2 where c and b are respective speed of the cyclist and bus
Also in 12 mins, distance traveled by cyc is 3x.
so 12= 3x/(b-c) and x= 4c (frm 1) so 1= c/(b-c) and b=2c........................3
put the value of b frm 3 in equation 2.
We get AB=12c
So now the total distance is 12c and bus speed is 2c. The bus travels in 6 min...
It's A COMPLETE WILD GUESS..!! I was not able to get answer in 2 min..Let me knw the OA and OE.
Re: test m08 question n18 [#permalink]
30 Apr 2010, 00:21
Bunuel wrote:
Let's say the distance between the buses is \(d\). We want to determine \(Interval=\frac{d}{b}\), where \(b\) is the speed of bus. Let the speed of cyclist be \(c\).
\(Interval=\frac{d}{b}=\frac{6b}{b}=6\)
Answer: 6 minutes.
Hope it helps.
Thanks for the explanation. Please clarify the following doubts. Aren't we calculating the interval between 2 buses that move towards each other? If yes, then would the interval not be 6b/b+b ?
Re: test m08 question n18 [#permalink]
30 Apr 2010, 00:59
3
This post received KUDOS
Expert's post
Fiver wrote:
Bunuel wrote:
Let's say the distance between the buses is \(d\). We want to determine \(Interval=\frac{d}{b}\), where \(b\) is the speed of bus. Let the speed of cyclist be \(c\).
\(Interval=\frac{d}{b}=\frac{6b}{b}=6\)
Answer: 6 minutes.
Hope it helps.
Thanks for the explanation. Please clarify the following doubts. Aren't we calculating the interval between 2 buses that move towards each other? If yes, then would the interval not be 6b/b+b ?
Not sure I understood your question...
Anyway: question asks "what is the time interval between consecutive buses". Or time intervals between subsequent bus arrivals to a given bus stop (some static point). Which is: constant distance between two subsequent buses divided by the constant rate of these buses d/b. After some calculations we've gotten that d=6b, hence d/b=6b/b=6. _________________
Re: test m08 question n18 [#permalink]
02 Apr 2012, 19:05
Bunuel wrote:
Fiver wrote:
Bunuel wrote:
Let's say the distance between the buses is \(d\). We want to determine \(Interval=\frac{d}{b}\), where \(b\) is the speed of bus. Let the speed of cyclist be \(c\).
\(Interval=\frac{d}{b}=\frac{6b}{b}=6\)
Answer: 6 minutes.
Hope it helps.
Thanks for the explanation. Please clarify the following doubts. Aren't we calculating the interval between 2 buses that move towards each other? If yes, then would the interval not be 6b/b+b ?
Not sure I understood your question...
Anyway: question asks "what is the time interval between consecutive buses". Or time intervals between subsequent bus arrivals to a given bus stop (some static point). Which is: constant distance between two subsequent buses divided by the constant rate of these buses d/b. After some calculations we've gotten that d=6b, hence d/b=6b/b=6.
Thanks bunnel for the explanation. But I have a doubt here. what is the time interval between consecutive buses? Isn't it the time interval between consecutive buses going in one direction. If that is the case then ans should be 12 min. Thanks. _________________
Re: test m08 question n18 [#permalink]
02 Apr 2012, 21:44
2
This post received KUDOS
1
This post was BOOKMARKED
shadabkhaniet wrote:
Thanks bunnel for the explanation. But I have a doubt here. what is the time interval between consecutive buses? Isn't it the time interval between consecutive buses going in one direction. If that is the case then ans should be 12 min. Thanks.
yeah if you standing at a busstop then whats the time interval of arrival of bus.--> you may take the question this way.
use relative velocity:
vel of bus=a vel of cyclist=b distance between them=d
now, d=12(a-b)=4(a+b)
hence d=6a so time interval is d/a=6 min
hope this clarifies...!! _________________
Practice Practice and practice...!!
If my reply /analysis is helpful-->please press KUDOS If there's a loophole in my analysis--> suggest measures to make it airtight.
Re: test m08 question n18 [#permalink]
02 Apr 2012, 21:54
kraizada84 wrote:
shadabkhaniet wrote:
Thanks bunnel for the explanation. But I have a doubt here. what is the time interval between consecutive buses? Isn't it the time interval between consecutive buses going in one direction. If that is the case then ans should be 12 min. Thanks.
yeah if you standing at a busstop then whats the time interval of arrival of bus.--> you may take the question this way.
use relative velocity:
vel of bus=a vel of cyclist=b distance between them=d
now, d=12(a-b)=4(a+b)
hence d=6a so time interval is d/a=6 min
hope this clarifies...!!
Thanks kraizada84 for explanation, but still yeah if you standing at a busstop then whats the time interval of arrival of bus.--> you may take the question this way. not making sense to me. If you are standing at a bus stop then the interval of arrival of bus will be in one direction only. But here we are calculating for both direction.
Re: test m08 question n18 [#permalink]
02 Apr 2012, 23:22
2
This post received KUDOS
You see in ONE DIRECTION, the distance between two buses is "d", the speed of the buses is "b"(lets just say its km/minute). So to find this interval, we take this distance divided by speed of bus(all in ONE DIRECTION). so d/b.
Now through algebra 12(a-b)=4(a+b) , we find that distance "d" is equal to "6b". remember d is distance between two buses in ONE DIRECTION. And so we do the division and get the answer 6 minutes.
Just because we do this algebra equation d=12(a-b)=4(a+b), doesn't mean that the nature of b,c or d has changed. It stays true to its original meaning.
No idea what else can clear up your confusion :S _________________
Please give KUDOS if you find that my post adds value! Thank you!!
Re: test m08 question n18 [#permalink]
02 Apr 2012, 23:51
1
This post received KUDOS
Expert's post
shadabkhaniet wrote:
Bunuel wrote:
Fiver wrote:
Thanks for the explanation. Please clarify the following doubts. Aren't we calculating the interval between 2 buses that move towards each other? If yes, then would the interval not be 6b/b+b ?
Not sure I understood your question...
Anyway: question asks "what is the time interval between consecutive buses". Or time intervals between subsequent bus arrivals to a given bus stop (some static point). Which is: constant distance between two subsequent buses divided by the constant rate of these buses d/b. After some calculations we've gotten that d=6b, hence d/b=6b/b=6.
Thanks bunnel for the explanation. But I have a doubt here. what is the time interval between consecutive buses? Isn't it the time interval between consecutive buses going in one direction. If that is the case then ans should be 12 min. Thanks.
Consecutive buses mean consecutive buses in one direction, how else? So, if the distance between two consecutive buses is \(d\) and the rate of the bus is \(b\) then \(Interval=\frac{d}{b}\).
Re: test m08 question n18 [#permalink]
03 Apr 2012, 01:03
Bunuel wrote:
shadabkhaniet wrote:
Bunuel wrote:
Not sure I understood your question...
Anyway: question asks "what is the time interval between consecutive buses". Or time intervals between subsequent bus arrivals to a given bus stop (some static point). Which is: constant distance between two subsequent buses divided by the constant rate of these buses d/b. After some calculations we've gotten that d=6b, hence d/b=6b/b=6.
Thanks bunnel for the explanation. But I have a doubt here. what is the time interval between consecutive buses? Isn't it the time interval between consecutive buses going in one direction. If that is the case then ans should be 12 min. Thanks.
Consecutive buses mean consecutive buses in one direction, how else? So, if the distance between two consecutive buses is \(d\) and the rate of the bus is \(b\) then \(Interval=\frac{d}{b}\).
Hope it helps.
thanks bunnel and anyonym for explanation. +1 _________________
Re: A man cycling along the road noticed that every 12 minutes [#permalink]
30 Apr 2012, 12:28
Hi Bunuel,
This is regarding the solution you gave:
Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;
Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;
d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.
Interval=\frac{d}{b}=\frac{6b}{b}=6
Answer: B (6 minutes).
when you say distance between 2 buses is d, you mean to buses that start at opposite ends right? ex. after 12 mins (POINT A)starting point for busA --------------cyclist(busA meets him here)-----------------staring point for busB -------------------------distance d -----------------------
then how is following possible coz d is the total distance not the distance between busA staring point and meeting point with cyclist. Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;
Plus, is the question asking for interval between when 2 buses leave staring point of busA(POINT A)?
Re: A man cycling along the road noticed that every 12 minutes [#permalink]
30 Apr 2012, 23:36
Expert's post
kartik222 wrote:
Hi Bunuel,
This is regarding the solution you gave:
Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;
Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;
d=12b-12c=4b+4c, --> b=2c, --> d=12b-6b=6b.
Interval=\frac{d}{b}=\frac{6b}{b}=6
Answer: B (6 minutes).
when you say distance between 2 buses is d, you mean to buses that start at opposite ends right? ex. after 12 mins (POINT A)starting point for busA --------------cyclist(busA meets him here)-----------------staring point for busB -------------------------distance d -----------------------
then how is following possible coz d is the total distance not the distance between busA staring point and meeting point with cyclist. Every 12 minutes a bus overtakes cyclist: \frac{d}{b-c}=12, d=12b-12c;
Plus, is the question asking for interval between when 2 buses leave staring point of busA(POINT A)?
thanks,
No, the distance between the buses is \(d\) means that \(d\) is the distance between two subsequent buses. _________________
Re: A man cycling along the road noticed that every 12 minutes [#permalink]
02 May 2012, 22:02
Can I assume that since Cyclist is meeting an oncoming bus every 4 minutes, his speed is 4km/hr? or lets assume that a bus crosses him every 12 minutes coming from back and in 4 minutes coming from front. Thus cumulative speed is 16km/hr however cyclist himself is also moving forward @4km/hr. Thus net effect is 12km/hr. Beyond that, I am confused.
Re: A man cycling along the road noticed that every 12 minutes [#permalink]
03 May 2012, 11:21
Expert's post
manjeet1972 wrote:
Can I assume that since Cyclist is meeting an oncoming bus every 4 minutes, his speed is 4km/hr? or lets assume that a bus crosses him every 12 minutes coming from back and in 4 minutes coming from front. Thus cumulative speed is 16km/hr however cyclist himself is also moving forward @4km/hr. Thus net effect is 12km/hr. Beyond that, I am confused.
No you can not assume that. Please refer to the solutions given above. _________________
Re: A man cycling along the road noticed that every 12 minutes [#permalink]
04 May 2012, 19:13
4
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
manjeet1972 wrote:
Can I assume that since Cyclist is meeting an oncoming bus every 4 minutes, his speed is 4km/hr? or lets assume that a bus crosses him every 12 minutes coming from back and in 4 minutes coming from front. Thus cumulative speed is 16km/hr however cyclist himself is also moving forward @4km/hr. Thus net effect is 12km/hr. Beyond that, I am confused.
I am not sure how you are assuming speeds, but if you are looking for a relatively theoretical solution, you can think in this way:
Say the cyclist is stationary at a point. Buses are coming from opposite directions (same speed, same time interval). A bus will meet the cyclist every t minutes from either direction. Let's say, a bus from each direction just met him. After t minutes, 2 more buses from opposite directions will meet him again and so on...
Now if the cyclist starts moving, (cyclist speed = c and bus speed = b), the ratio of the relative speeds of the buses is the inverse of the ratio of time taken i.e. it will be 4:12
(b-c):(b+c) = 4:12 which gives you c = (1/2)b
This means that the bus travelling at a relative speed which is half its usual speed (b-c = b/2) takes 12 minutes to meet the man. If it were travelling at its usual speed, it would have taken 12/2 = 6 mins to meet the man. _________________
The “3 golden nuggets” of MBA admission process With ten years of experience helping prospective students with MBA admissions and career progression, I will be writing this blog through...
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...