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31 Jan 2022, 05:15
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C
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Difficulty:
95%
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Question Stats:
54% (03:11) correct
46%
(03:12)
wrong
based on 94
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Two cities X and Y lie on a straight line. Two men P and Q left simultaneously for Y and X from X and Y respectively. P reaches Y and immediately turns around and moves towards X. On reaching X, again he turns around and moves towards Y. This kind of movement continues indefinitely. Q also travels in a similar manner. The distance between X and Y is 1000m and the ratio of the speeds of P and Q is 3:2. What is the distance traveled by P when he meets Q for the fourth time?
(A) 5,600M
(B) 4,800M
(C) 4,200M
(D) 4,000M
(E) 3,200M
Are You Up For the Challenge: 700 Level Questions
(A) 5,600M
(B) 4,800M
(C) 4,200M
(D) 4,000M
(E) 3,200M
Are You Up For the Challenge: 700 Level Questions
Jagmeister
Joined: 24 Feb 2021
Last visit: 19 Aug 2023
Posts: 169
Given Kudos: 137
Location: India
Concentration: Technology, Entrepreneurship
Schools: Fuqua '25 (WA$$) HBS '25 (D) Stanford '25 (D) Sloan '25 (D) Haas '25 (WL) Darden '25 (A) Ross '25 (WL) Marshall '25 (WA$$$) McCombs '25 (D) Tuck '25 (WL)
GMAT 1: 720 Q50 V37 (Online)
GMAT 2: 750 Q50 V42 (Online)
GPA: 4
Schools: Fuqua '25 (WA$$) HBS '25 (D) Stanford '25 (D) Sloan '25 (D) Haas '25 (WL) Darden '25 (A) Ross '25 (WL) Marshall '25 (WA$$$) McCombs '25 (D) Tuck '25 (WL)
GMAT 2: 750 Q50 V42 (Online)
Posts: 169
31 Jan 2022, 05:30
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I believe the answer is (C) 4200
This is my approach:
In the beginning P and Q are 1000m apart and start moving towards each other at speeds in the ratio 3:2 respectively.
So when they meet for the first time:
Since ratio of speeds = ratio of distance, therefore-
distance covered by P = 600m
distance covered by Q= 400m
now for them to meet the next time, they would have to cover 2000m in total (1000m in total in the opposite direction (after their meeting) till they reach their respective ends and then 1000m in total towards each other, till they meet again)
again, using the same ratio logic, distance covered between 1st and 2nd meeting:
distance covered by P = 1200m
distance covered by Q= 800m
This will also be the distance travelled by them when they meet for the 3rd time and for the 4th time.
therefore total distance covered by P = 600+1200+1200+1200 = 4200
This is my approach:
In the beginning P and Q are 1000m apart and start moving towards each other at speeds in the ratio 3:2 respectively.
So when they meet for the first time:
Since ratio of speeds = ratio of distance, therefore-
distance covered by P = 600m
distance covered by Q= 400m
now for them to meet the next time, they would have to cover 2000m in total (1000m in total in the opposite direction (after their meeting) till they reach their respective ends and then 1000m in total towards each other, till they meet again)
again, using the same ratio logic, distance covered between 1st and 2nd meeting:
distance covered by P = 1200m
distance covered by Q= 800m
This will also be the distance travelled by them when they meet for the 3rd time and for the 4th time.
therefore total distance covered by P = 600+1200+1200+1200 = 4200
10 Aug 2023, 04:56
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Bunuel
We can use ratios to directly get the answer.
X (P)-->---------------- 1000 m --------------<--(Q) Y
The first meeting happens when they together cover 1000 m.
Thereafter they reached their own destinations and again travelled towards each other covering a distance of 2000 m to meet (since their last meeting). Same will be true for their 3rd and 4th meetings. They will cover total 2000 m every time to meet again.
So till the 4th meeting, they would have covered a total of 7000 m together in the ratio 3:2. Then the multiplier is 1400.
Hence, P would have covered 3*1400 = 4200 m while Q would have covered 2*1400 = 2800 m
Answer (C)
Consider what happens when their speeds are in the ratio 4:1 instead. Why?
Check here to see how to use ratios for TSD: https://youtu.be/7ASEIvxYPCM
If you are not comfortable with ratios, check here: https://youtu.be/5ODENGG5dvc
