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23 Sep 2023, 03:32
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D
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Difficulty:
15%
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Question Stats:
86% (01:45) correct
14%
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wrong
based on 202
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A, B, C, and D, working together, can complete a task in 2 hours. When A and B pair up, they are able to finish the same task in 6 hours. C, working alone, can complete it in 9 hours. How many hours will it take for D to complete the task by himself?
A. 2 hours
B. 3 hours
C. 6 hours
D. 4.5 hours
E. 9 hours
A. 2 hours
B. 3 hours
C. 6 hours
D. 4.5 hours
E. 9 hours
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Mech_Warrior
Joined: 25 Dec 2022
Last visit: 05 Aug 2024
Posts: 8
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Given Kudos: 7
Location: India
Schools: ISB '25 (S) Oxford Said'25 IE Sep'24 intake
GMAT 1: 590 Q48 V23
GMAT 2: 700 Q45 V41
23 Sep 2023, 03:58
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Bunuel
Time Rate Work (LCM of Time)
A+B+C+D 2 9 18
A+B 6 3 18
C 9 2 18
Rate of D (9-(3+2))
D 4.5 4 18
Ans- D
23 Sep 2023, 03:59
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Bunuel
Assume ➔ A does 'a' unit of work per hour, B does 'b' unit of work per hour, C does 'c' unit of work per hour, and D does 'd' unit of work per hour.
..A, B, C, and D, working together, can complete a task in 2 hours..
Amount of work done by A, B, C, and D in 2 hours = Effort needed to complete the task = 2a + 2b + 2c + 2d
..When A and B pair up, they are able to finish the same task in 6 hours..
Amount of work done by A and B in 6 hours = Effort needed to complete the task = 6a + 6b
..working alone, can complete it in 9 hours..
Amount of work done by C in 9 hours = Effort needed to complete the task = 9c
The effort required to complete the task in all three cases is the same. Therefore -
2a + 2b + 2c + 2d = 6a + 6b = 9c
Equating 6a + 6b = 9c, we get
2a + 2b = 3c
Equating 2a + 2b + 2c + 2d = 9c, we get
3c + 2c + 2d = 9c
2d = 9c - 5c
2d = 4c
d = 2c
Therefore D is twice as efficient as C is. Hence, D will require half the time required by C.
Time required by D = \(\frac{1}{2} * 9 = 4.5\)
Option D
