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Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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21 Mar 2017, 04:59
Question Stats:
67% (03:00) correct 33% (03:09) wrong based on 181 sessions
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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21 Mar 2017, 11:52
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Dwight = First Shift
Remaining Work = Total Work (Let us represent the total work as 1) = 1
Diwght completes 1/4th of the remaining work
Remaining Work = 1  1/4 = 3/4
Mose = First Shift
Remaining Work = 3/4
Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8
Remaining work = 3/4  1/8 = 5/8
Dwight = Second Shift
Remaining Work = 5/8
Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32
Remaining work = 5/8  5/32 = 15/32
Mose = Second Shift
Remaining Work = 15/32
Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64
Remaining work = 15/32  5/64 = 25/64
Dwight = Third Shift
Remaining Work = 25/64
Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256
Remaining work = 25/64  25/256 = 75/256
Work on the barn that is left to finish when Mose begins his third shift = 75/256
Answer is D. 75/256



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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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12 Apr 2017, 13:57
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quantumliner wrote: Dwight = First Shift
Remaining Work = Total Work (Let us represent the total work as 1) = 1
Diwght completes 1/4th of the remaining work
Remaining Work = 1  1/4 = 3/4
Mose = First Shift
Remaining Work = 3/4
Mose completes 1/6th of the remaining work = 3/4 * 1/6 = 1/8
Remaining work = 3/4  1/8 = 5/8
Dwight = Second Shift
Remaining Work = 5/8
Diwght completes 1/4th of the remaining work = 5/8 * 1/4 = 5/32
Remaining work = 5/8  5/32 = 15/32
Mose = Second Shift
Remaining Work = 15/32
Mose completes 1/6th of the remaining work = 15/32 * 1/6 = 5/64
Remaining work = 15/32  5/64 = 25/64
Dwight = Third Shift
Remaining Work = 25/64
Diwght completes 1/4th of the remaining work = 25/64 * 1/4 = 25/256
Remaining work = 25/64  25/256 = 75/256
Work on the barn that is left to finish when Mose begins his third shift = 75/256
Answer is D. 75/256 I'm not sure if I could do this in, lets say, 90 seconds... Instead, I identified the path: Work remained D1 (11/4) M1 (11/4)  (11/4)x1/6 = (11/4)(11/6) = (3/4)(5/6) then: D2 (3/4)(5/6)(3/4) M2 (3/4)(5/6)(3/4)(5/6) D3 (3/4)(5/6)(3/4)(5/6)(3/4) = 75/256



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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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12 Apr 2017, 14:25
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Bunuel wrote: Dwight and Mose decide to build a new barn on their farm, and they begin to work in alternating shifts, with Dwight taking the first shift. During each of his shifts, Dwight does 1/4 of the remaining work. During each of his shifts, Mose does 1/6 of the remaining work. How much of the barn is left to finish when Mose begins his third shift?
A. 1/24 B. 5/36 C. 25/72 D. 75/256 E. 255/512 Let total work be 256 units Work remaining at the 5th shift (because Mose's third shift will be the sixth shift) = (256) *(3/4)*(5/6)*(3/4)*(5/6)*(3/4) = 75 Hence the answer is D
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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12 Apr 2017, 14:30
This seems like it would take too long
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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12 Apr 2017, 14:31
gmathopeful19 wrote: This seems like it would take too long
Posted from my mobile device It wouldn't if you assume the work to be of 256 units.
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Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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16 Jun 2017, 18:46
Why do you have to multiply the remaining amount of work by the amount being completed (as opposed to subtract)?



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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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16 Jun 2017, 21:53
This is something that we have to keep dividing by 4 and 6 (since 3/4 work is left, and 5/6 work is left), so better take a number which has atleast three 4's and three 6's. So lets take the initial barn work to be 4^3 * 6^3.
First shift: Dwight does = 1/4 and work remaining = 3/4 * 4^3 * 6^3 = 3 * 4^2 * 6^3 Then Mose does = 1/6 and work remaining = 5/6 * 3 * 4^2 * 6^3 = 3 * 5 * 4^2 * 6^2
Second shift Dwight does= 1/4 and remaining = 3/4 * 3 * 5 * 4^2 * 6^2 = 3^2 * 4 * 5 * 6^2 Mose does = 1/6 and work remaining = 5/6 * 3^2 * 4 * 5 * 6^2 = 3^2 * 5^2 * 4 * 6
Third Shift Dwight does = 1/4 and work remaining for Mose = 3/4 * 3^2 * 5^2 * 4 * 6 = 3^3 * 5^2 * 6
So the fraction of work left = (3^3 * 5^2 * 6)/(4^3 * 6^3) = (27*25)/(64*36) = 75/256
Thus D is answer



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Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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12 Dec 2017, 23:35
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Let the work to be completed be 1. D completes 1/4 of the remaining work. Therefore work remaining is \((11/4)\). M completes 1/6 of the remaining work. Hence \([(11/4)(11/4)(1/6)]\). Therefore work remaining is \((11/4)(11/6)\).
Hence work remaining when M starts work 3rd time is \((11/4)^3*(11/6)^2 = 75/256\)



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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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17 Dec 2017, 03:39
PerfectScores wrote: gmathopeful19 wrote: This seems like it would take too long
Posted from my mobile device It wouldn't if you assume the work to be of 256 units. Can you explain why we assume the work to be of 256 units please? Thank a lot.



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Re: Dwight and Mose decide to build a new barn on their farm, and they beg [#permalink]
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17 Dec 2017, 06:08
khiemchii wrote: PerfectScores wrote: gmathopeful19 wrote: This seems like it would take too long
Posted from my mobile device It wouldn't if you assume the work to be of 256 units. Can you explain why we assume the work to be of 256 units please? Thank a lot. Hi, Lets say total work is 256 . D does 1/4 and M does 1/ of the remaining Unit . Ist Attempt: D = 1/4*256 = 64 , M = (25664)*1/6 = 32 2nd Attempt: D = (256  96)*1/4 = 40 , M = (256  136) *1/6= 20 3rd Attempt: D = (256156)*1/4= 25 At this point work remaining for M is 75 out of 256 . Hence 75/256 is answer
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Re: Dwight and Mose decide to build a new barn on their farm, and they beg
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