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Joined: 11 Jan 2019
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Three workers, A, B, and C, can complete a certain task in 10, 5 and x
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12 Jan 2019, 17:28
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Hello I am new to GMAT club, and I am unsure if this is the right place to post this, but I am having trouble with what seems like a simple math problem.
Three workers, A, B, and C, can complete a certain task in 10, 5 and x hours respectively. A starts working alone and 2 hours later B joins. After another 2 hours joins C. After that A, B, and C together complete the task in 15 minutes. What is the value of x ? Answer Choices: 1 1.25 2 2.5 4
I got the answer 2 through plugging in different possible answers, but I do not understand how 1/4*(1/10+1/5+1/x) gives you this answer without plugging in different possibilities.



Senior Manager
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Re: Three workers, A, B, and C, can complete a certain task in 10, 5 and x
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13 Jan 2019, 01:37
A (alone) completes the task in 10 hours, so in 1 hour he does 1/10 of the task B (alone) completes the task in 5 hours, so in 1 hour he does 1/5 of the task C (alone) completes the task in x hours, so in 1 hour he does 1/x of the task A and B combined do : 1/10 + 1/5 = 3/10 of the task in 1 hour hour A, B and C combined do: 1/10 + 1/5 + 1/x = 3/10 + 1/x of the task in one hour A starts work and works for 2 hours, so he completes 1/10* 2 = 1/5 of the task Then A & B work for next 2 hours and complete 3/10*2 = 3/5 of the task Remaining uncompleted part = 1  (1/5 + 3/5) = 1/5 This remaining task is done by A, B and C combined in 15 mins. 1/5 = (1/10 + 1/5 + 1/x)*15/60 so x =2
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Joined: 24 Nov 2018
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Location: India

Re: Three workers, A, B, and C, can complete a certain task in 10, 5 and x
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13 Jan 2019, 22:33
Pick a multiple of 5 and 10 for easy calculation. Total work can be 50 The efficiency of a = 50/10= 5 The efficiency of a = 50/5=10 The efficiency of a = 50/x
First hour: only a is working 5 units of work Second hour: only a is working 5 units of work Third hour: a: 5 units of work b: 10 units of work Fourth hour: a: 5 units of work b: 10 units of work Total  40 units of work done, remaining unit 5040=10
10/ 5+10+(50/x)= 15/60 ie: Remaing work / efficency of all = time
25x=50 x= 2




Re: Three workers, A, B, and C, can complete a certain task in 10, 5 and x
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13 Jan 2019, 22:33






