Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Jan 2010
Posts: 300

Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
27 Apr 2012, 14:07
Question Stats:
57% (02:02) correct 43% (01:23) wrong based on 303 sessions
HideShow timer Statistics
Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving? A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 22 Jan 2012
Posts: 34

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
27 Apr 2012, 15:07
For this question , we will start with the body who is the slowest i.e. 3m/sec.
Since the questions asks us when all the three bodies are going to meet , so assume the time t is reqduired to do this Distance travelled by I body: 3t Distance travelled by II body: 5t Distance travelled by III body: 9t
the distances should be equal to meet , and that is possible because of a circular track , length of the track: 60m
Keep this is mind , for circular track The point on the circular track = n * length of the track + remaining distance where n is a positive integer
Like if someone travels from point Z on the track 200 m then actually he is far from point Z by 20m . As ,200 = 3*60 +20
Now i inserted the values : A: 30 secs I=3*30=90 = one length of track +30 ; II=5*30=150 = 2 lenth of track + 30; III= 9*30 =270 = 4 lenth of track +30;
so everyone is at 30 m after 30 secs. Hence A is the answer.



Senior Manager
Joined: 21 Jan 2010
Posts: 300

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
27 Apr 2012, 18:45
thanks , probably this is the quickest way for this , but any algebric way to handle this?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
27 Apr 2012, 19:25
vdadwal wrote: Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds A  3 m/s, B  5 m/s, C  9 m/s When will they meet if they are moving in the same direction? When B covers one (or multiple) complete circle more than A and C also covers one (or multiple) complete circle more than A. B's speed is 2 m/s more than A so he will take 60/2 = 30 s to complete one full circle more than A. In 60 secs he will cover 2 circles more than A and so on... C's speed is 6 m/s more than A so he will take 60/6 = 10 s to complete one full circle more than A. In 20 secs he will cover 2 circles more than A and in 30 sec he will cover 3 circles more than A. So in 30 s, all A, B and C will be at the same point. Answer A
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Joined: 24 Aug 2009
Posts: 481
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
25 Aug 2012, 11:37
Hi Karishma, After calculating Relative speed of B & C over A. We can take LCM of time taken to complete one round by B & C to find out when all three will meet. This shortcut is preferred once anyone has mastered the logic as suggested by karishma
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Director
Joined: 22 Mar 2011
Posts: 605
WE: Science (Education)

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
25 Aug 2012, 12:23
vdadwal wrote: Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds If they all meet after T seconds, it means they covered the distances 3T, 5T, and 9T respectively. Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 60m. So, 2T, 4T, and 6T must all be multiples of 60. 2T multiple of 60 means T multiple of 30. The smallest T with this property is 30 and is on the list of answers. Answer A.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
27 Aug 2012, 22:41
fameatop wrote: Hi Karishma,
After calculating Relative speed of B & C over A. We can take LCM of time taken to complete one round by B & C to find out when all three will meet. This shortcut is preferred once anyone has mastered the logic as suggested by karishma Yes, you are right. You get that the time taken by B to complete one extra circle is 30 secs and time taken by C to complete one extra circle is 10 secs. You take their LCM which is 30 secs. The theory explains why you should take the LCM.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 24 Jul 2011
Posts: 72
Location: India
Concentration: Strategy, General Management
WE: Asset Management (Manufacturing)

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
29 Aug 2012, 08:34
Speed of A,B and C are 3, 5, 9 m/s respectively. Considering A&B: Speed of B is (53)=2 m/s more than that of A. So with this relative speed it will take 60/2= 30 sec to cover the full length. Considering B&C: Relative speed is (95)=4 m/s. So, B&C will meet after every 60/4=15 sec. Considering A&C: Relative speed is (93)=6 m/s. So, A&C will meet after every 60/6=10 sec. The time when all three will meet together is the LCM of values 30, 15 and 10. That is 30. Because 30=30*1 ( So A,B meet) 30=15*2 (So, B,C meet) 30=10*3 (So, A,C meet) So, after 30 sec they will meet again. A Followup Question: When will A,B and C meet together at the start point?
_________________
My mantra for cracking GMAT: Everyone has inborn talent, however those who complement it with hard work we call them 'talented'.
+1 Kudos = Thank You Dear Are you saying thank you?



Manager
Joined: 26 Feb 2012
Posts: 104
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
18 Aug 2013, 01:34
VeritasPrepKarishma wrote: vdadwal wrote: Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds A  3 m/s, B  5 m/s, C  9 m/s When will they meet if they are moving in the same direction? When B covers one (or multiple) complete circle more than A and C also covers one (or multiple) complete circle more than A. B's speed is 2 m/s more than A so he will take 60/2 = 30 s to complete one full circle more than A. In 60 secs he will cover 2 circles more than A and so on... C's speed is 6 m/s more than A so he will take 60/6 = 10 s to complete one full circle more than A. In 20 secs he will cover 2 circles more than A and in 30 sec he will cover 3 circles more than A. So in 30 s, all A, B and C will be at the same point. Answer A Hi Karishma I have lost control over my understanding though u mentioned very clearly. Requesting you to again depicts the same for me. Also the theory behind the logic and any other question of similar kind. Rgds Prasannajeet



Senior Manager
Joined: 10 Jul 2013
Posts: 318

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
18 Aug 2013, 03:11
Bluelagoon wrote: Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds i like to back solve it: (it takes at most 40 seconds) i explained my way below: For circular distance of 60 meter, 60,120,180,240 all end in the same point for body A , 30 * 3 = 90 m = 60 + 30 m (so 30m ahead from the starting point) for body, B, 30 * 5 = 150 m = 120 + 30 m (so 30m ahead from the starting point) for body C, 30 * 9 = 270 m = 240 + 30 m (so 30m ahead from the starting point) Everyone 30m ahead of the starting point after 30 sec. i am lucky enough that the 1st answer satisfies my findings.
_________________
Asif vai.....



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
19 Aug 2013, 05:12
prasannajeet wrote: VeritasPrepKarishma wrote: vdadwal wrote: Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds A  3 m/s, B  5 m/s, C  9 m/s When will they meet if they are moving in the same direction? When B covers one (or multiple) complete circle more than A and C also covers one (or multiple) complete circle more than A. B's speed is 2 m/s more than A so he will take 60/2 = 30 s to complete one full circle more than A. In 60 secs he will cover 2 circles more than A and so on... C's speed is 6 m/s more than A so he will take 60/6 = 10 s to complete one full circle more than A. In 20 secs he will cover 2 circles more than A and in 30 sec he will cover 3 circles more than A. So in 30 s, all A, B and C will be at the same point. Answer A Hi Karishma I have lost control over my understanding though u mentioned very clearly. Requesting you to again depicts the same for me. Also the theory behind the logic and any other question of similar kind. Rgds Prasannajeet Check out this post on circular motion: http://www.veritasprep.com/blog/2012/08 ... ncircles/See if this helps else I will try to explain more in detail.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Joined: 13 May 2013
Posts: 430

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
19 Aug 2013, 14:01
Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds
From the onset I kind of figured you could solve with LCM's but I wasn't entirely sure why. I tried solving by figuring out how long it would take each of them to make one complete revolution and keep counting until their times aligned but I think that is incorrect because we're trying to figure out how long it takes for them to "meet up" we cannot solve that way. Is this correct?
If that is the case, then we need to figure out their relative speeds to determine when each body (let's call them A, B, C for the slow, medium and fast objects respectively) reaches the other.
B's relative rate to A is 53 = 2m/second so it takes B 30 seconds to move 60 meters away from A. In other words, at the 30 second mark, A and B are next to one another. A has traveled 90 meters and B has traveled 150 meters.
C's relative rate to A is 93 = 6m/second so it takes C 10 seconds to move 60 meters away from A. Every 10 seconds, it moves 60 meters (one full revolution) away from A. In 30 seconds (the time it takes A and B to meet up) it is 3 full revolutions ahead of A but is also next to it on the circle.
ANSWER A. 30 seconds.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
20 Aug 2013, 21:37
WholeLottaLove wrote: Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds B. 60 seconds C. 15 seconds D. 10 seconds E. 25 seconds
From the onset I kind of figured you could solve with LCM's but I wasn't entirely sure why. I tried solving by figuring out how long it would take each of them to make one complete revolution and keep counting until their times aligned but I think that is incorrect because we're trying to figure out how long it takes for them to "meet up" we cannot solve that way. Is this correct?
If that is the case, then we need to figure out their relative speeds to determine when each body (let's call them A, B, C for the slow, medium and fast objects respectively) reaches the other.
B's relative rate to A is 53 = 2m/second so it takes B 30 seconds to move 60 meters away from A. In other words, at the 30 second mark, A and B are next to one another. A has traveled 90 meters and B has traveled 150 meters.
C's relative rate to A is 93 = 6m/second so it takes C 10 seconds to move 60 meters away from A. Every 10 seconds, it moves 60 meters (one full revolution) away from A. In 30 seconds (the time it takes A and B to meet up) it is 3 full revolutions ahead of A but is also next to it on the circle.
ANSWER A. 30 seconds. LCM of time works for a question of a different type: When will they meet for the first time AT THE STARTING POINT after they started moving? Time take by A to cover a circle = 60/3 = 20 sec Time taken by B to cover a circle = 60/5 = 12 sec Time taken by C to cover a circle = 60/9 sec So every 20 sec, A will be at the starting point. Every 12 secs B will be at the starting point. Every 60/9 sec, C will be at the starting point. Taking their LCM, we get 60. So every 60 sec, all three will be at the starting point. All meet for the first time at the starting point after they start moving after 60 sec.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



NonHuman User
Joined: 09 Sep 2013
Posts: 7010

Re: Three bodies A, B and C start moving around a circular track [#permalink]
Show Tags
19 Jan 2018, 16:50
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




Re: Three bodies A, B and C start moving around a circular track
[#permalink]
19 Jan 2018, 16:50






