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05 May 2019, 20:27
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
14% (03:15) correct
86%
(02:43)
wrong
based on 22
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History
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Not Attempted Yet
Three friends A, B, and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B, and C?
A. 5 : 4 : 2
B. 4 : 3 : 2
C. 5 : 4 : 3
D. 3 : 2 : 1
E. 5 : 3 : 1
A. 5 : 4 : 2
B. 4 : 3 : 2
C. 5 : 4 : 3
D. 3 : 2 : 1
E. 5 : 3 : 1
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05 May 2019, 21:09
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Let the length of track is 'L'
When A finished lap 1, assume B is at L-x and C at L-2x
When A finished 3rd track, C must be at L-x or 2L-x (In both scenario he is at same position, as B was when A finished 1st lap)
Case 1
If C is in lap 1, when A finished his 3rd lap
3*(L-2x)= L-x
3L-6x=L-x
2L=5x
A:B:C=L:(L-x):(L-2x)
A:B:C=L : (L-{2L/5}) : (L-{4L/5}) = L : 3L/5 : L/5
A:B:C= 5:3:1
Case 2
If C is in lap 2, when A finished his 3rd lap
3*(L-2x)= 2L-x
3L-6x=2L-x
L=5x
A:B:C=L:(L-x):(L-2x)
A:B:C=L : (L-{L/5}) : (L-{2L/5}) = L : 4L/5 : 3L/5
A:B:C= 5:4:3
C and E both can be correct
When A finished lap 1, assume B is at L-x and C at L-2x
When A finished 3rd track, C must be at L-x or 2L-x (In both scenario he is at same position, as B was when A finished 1st lap)
Case 1
If C is in lap 1, when A finished his 3rd lap
3*(L-2x)= L-x
3L-6x=L-x
2L=5x
A:B:C=L:(L-x):(L-2x)
A:B:C=L : (L-{2L/5}) : (L-{4L/5}) = L : 3L/5 : L/5
A:B:C= 5:3:1
Case 2
If C is in lap 2, when A finished his 3rd lap
3*(L-2x)= 2L-x
3L-6x=2L-x
L=5x
A:B:C=L:(L-x):(L-2x)
A:B:C=L : (L-{L/5}) : (L-{2L/5}) = L : 4L/5 : 3L/5
A:B:C= 5:4:3
C and E both can be correct
udaypratapsingh99
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GMAT 1: 660 Q47 V34
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Schools: Fuqua '24 Harvard '24 LBS '24 NTU NUS Said '23 Ross '24 Sloan '24 Stanford '24 Tepper '24 Tuck '24 Wharton '24 Yale '24
GMAT 1: 660 Q47 V34
Posts: 395
06 May 2019, 04:26
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DisciplinedPrep
Think about the distance covered by each individual at a point of time and anchor the question around it.
Let track length be equal to T. When A completes a lap, let us assume B has run a distance of (t - d). At this time, C should have run a distance of (t - 2d).
After 3 laps C is in the same position as B was at the end of one lap. So, the position after 3t - 6d should be the same as t - d. Or, C should be at a distance of d from the end of the lap. C will have completed less than 3 laps (as he is slower than A), so he could have traveled a distance of either t - d or 2t - d.
=> 3t - 6d = t - d
=> 2t = 5d
=> d = 0.4t
The distances covered by A, B and C when A completes a lap will be t, 0.6t and 0.2t respectively. Or, the ratio of their speeds is 5 : 3 : 1.
In the second scenario, 3t - 6d = 2t - d => t = 5d => d = 0.2t.
The distances covered by A, B and C when A completes a lap will be t, 0.8t and 0.6t respectively. Or, the ratio of their speeds is 5 : 4 : 3.
The question is " Find the ratio of the speeds of A, B and C?"
The ratio of the speeds of A, B and C is either 5 : 3 : 1 or 5 : 4 : 3.
Hence, the answer is 5 : 4 : 3
Choice C is the correct answer.
