Last visit was: 15 Dec 2024, 03:02 It is currently 15 Dec 2024, 03:02
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
pintukr
User avatar
Joined: 03 Jul 2022
Last visit: 12 Dec 2024
Posts: 1,332
Own Kudos:
922
 []
Given Kudos: 22
GMAT 1: 680 Q49 V34
Products:
My Reviews GMAT Club Tests
GMAT 1: 680 Q49 V34
Posts: 1,332
Kudos: 922
 []
Two runners A and B start running towards each other in a straight lin Updated on: 31 Jul 2022, 09:54
Originally posted by pintukr on 29 Jul 2022, 04:33.
Last edited by pintukr on 31 Jul 2022, 09:54, edited 2 times in total.
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

52% (04:00) correct 48% (02:50) wrong based on 25 sessions

History

Date
Time
Result
Not Attempted Yet
Two runners A and B start running towards each other in a straight line from points P and Q respectively. It is known that if they meet each other, or if they reach their starting positions they reverse their direction. Initially speed of A and B is in the ratio 1:2, but B halved his speed every time he reached point Q. What is the ratio of distance travelled by A to distance travelled by B till they meet for the 4th time?

A. 8:5
B. 9:4
C. 16:9
D. 19:16
E. 36:25

(adapted frpm varsitytutors)

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
ShowHide Answer
Official Answer
D
User avatar
somya95
User avatar
Joined: 14 Aug 2020
Last visit: 25 Feb 2023
Posts: 3
Given Kudos: 52
Location: India
WE:Information Technology (Computer Software)
Posts: 3
Kudos: 0
Two runners A and B start running towards each other in a straight lin 30 Jul 2022, 03:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is there a way to solve this problem quickly? Took ~5 mins to solve this.
User avatar
AnonymousSolvers
User avatar
Joined: 25 Jul 2022
Last visit: 23 Feb 2023
Posts: 1
Own Kudos:
1
Posts: 1
Kudos: 1
Two runners A and B start running towards each other in a straight lin 31 Jul 2022, 07:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1st time A and B meet: distance: A: 1/3 * PQ; B: 2/3*PQ
Then A and B turn back to P and Q, where B halved his speed with vA = vB
2nd time: distance: A: 1/2 * PQ; B: 1/2 * PQ
same method, 3rd time: A: 2/3 * PQ; B: 1/3 * PQ
4th: A: 4/5 * PQ; B: 1/5 * PQ.
ratio distance A:B = (1/3 *2 + 1/2 *2 + 2/3 *2 + 4/5) / (2/3 *2+ 1/2 *2+ 1/3 *2 + 1/5) = 19/16
User avatar
pintukr
User avatar
Joined: 03 Jul 2022
Last visit: 12 Dec 2024
Posts: 1,332
Own Kudos:
922
Given Kudos: 22
GMAT 1: 680 Q49 V34
Products:
My Reviews GMAT Club Tests
GMAT 1: 680 Q49 V34
Posts: 1,332
Kudos: 922
Two runners A and B start running towards each other in a straight lin 31 Jul 2022, 09:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
somya95

Two runners A and B start running towards each other in a straight line from points P and Q respectively. It is known that if they meet each other, or if they reach their starting positions they reverse their direction. Initially speed of A and B is in the ratio 1:2, but B halved his speed every time he reached point Q. What is the ratio of distance travelled by A to distance travelled by B till they meet for the 4th time?

A. 8:5
B. 9:4
C. 16:9
D. 19:16
E. 36:25

Here is another approach to solve this PS question

say, A starts from P
B starts from Q

Given, if they meet each other, or if they reach their starting positions they reverse their direction.

It essentially means that A and B travel towards each other, meet at M (say) and return to P and Q, respectively.
Post returning to Q, B halves his speed, but A maintains his original speed.
thus, covering a total distance equivalent to 2d


Now, P to M1 (meeting point 1) to P -->

A's speed : B's speed = 1:2
Distance (by A) = 2d/3; Distance (by B) = 4d/3..................Total distance covered = 2d..............(1)

then, P to M2 (meeting point 2) to P -->

A's speed : B's speed = 1:1 (ie, B halves his speed vis-a-vis previous speed)
Distance (by A) = 2d/2 = d; Distance (by B) = 2d/2 = d..................Total distance covered = 2d..............(2)

then, P to M3 (meeting point 3) to P -->

A's speed : B's speed = 1: 0.5 = 2:1 (ie, B halves his speed vis-a-vis previous speed)
Distance (by A) = 4d/3 ; Distance (by B) = 2d/3.............Total distance covered = 2d..............(3)

finally, P to M4 (meeting point 4) --> (Note : calculation only till 4th meeting point, ie, together distance = d, and NOT 2d)

A's speed : B's speed = 1: 0.25 = 4:1 (ie, B halves his speed vis-a-vis previous speed)
Distance (by A) = 4d/5 ; Distance (by B) = d/5.............Total distance covered = d..............(4)

Thus, we get

Distance (by A) : Distance (by B) = (2d/3 + d + 4d/3 + 4d/5) : (4d/3 + d + 2d/3 + d/5)
= (57d/15) : (48d/15)
= 57 : 48
= 19 : 16
(D) is the correct option

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderators:
Bunuel
Math Expert
97879 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3116 posts