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:

Three bodies A, B and C start moving around a circular track [#permalink]

Show Tags

27 Apr 2012, 14:07

1

This post received KUDOS

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

56% (02:44) correct
44% (01:42) wrong based on 219 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

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.

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
_________________

Re: Three bodies A, B and C start moving around a circular track [#permalink]

Show Tags

25 Aug 2012, 11:37

1

This post received KUDOS

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

Re: Three bodies A, B and C start moving around a circular track [#permalink]

Show Tags

25 Aug 2012, 12:23

2

This post received KUDOS

1

This post was BOOKMARKED

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.

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.
_________________

Re: Three bodies A, B and C start moving around a circular track [#permalink]

Show Tags

29 Aug 2012, 08:34

6

This post received KUDOS

4

This post was BOOKMARKED

Speed of A,B and C are 3, 5, 9 m/s respectively. Considering A&B: Speed of B is (5-3)=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 (9-5)=4 m/s. So, B&C will meet after every 60/4=15 sec.

Considering A&C: Relative speed is (9-3)=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 Follow-up 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?

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.

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.
_________________

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.

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 5-3 = 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 9-3 = 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.

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 5-3 = 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 9-3 = 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.
_________________

Re: Three bodies A, B and C start moving around a circular track [#permalink]

Show Tags

01 Nov 2014, 17:22

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.
_________________

Re: Three bodies A, B and C start moving around a circular track [#permalink]

Show Tags

18 Dec 2015, 06:56

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.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

There is without a doubt a stereotype for recent MBA grads – folks who are ambitious, smart, hard-working, but oftentimes lack experience or domain knowledge. Looking around and at...