Dwight and Mose decide to build a new barn on their farm, and they beg

Question

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

A. 1/24
B. 5/36
C. 25/72
D. 75/256
E. 255/512

leandrodijon · Accepted Answer

I'm not sure if I could do this in, lets say, 90 seconds... Instead, I identified the path: Work remained D1 (1-1/4) M1 (1-1/4) - (1-1/4)x1/6 = (1-1/4)(1-1/6) = (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 8-)

PerfectScores · Answer

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

quantumliner · Answer

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

gmathopeful19 · Answer

This seems like it would take too long

Posted from my mobile device

PerfectScores · Answer

It wouldn't if you assume the work to be of 256 units.

mrdlee23 · Answer

Why do you have to multiply the remaining amount of work by the amount being completed (as opposed to subtract)?

amanvermagmat · Answer

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

mjana89 · Answer

Let the work to be completed be 1.
D completes 1/4 of the remaining work. Therefore work remaining is  (1-1/4) .
M completes 1/6 of the remaining work. Hence    . Therefore work remaining is  (1-1/4)(1-1/6) .

Hence work remaining when M starts work 3rd time is  (1-1/4)^3*(1-1/6)^2 = 75/256

khiemchii · Answer

Can you explain why we assume the work to be of 256 units please?
Thank a lot.

anje29 · Answer

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 = (256-64)*1/6 = 32

2nd Attempt:

D = (256 - 96)*1/4 = 40 , M = (256 - 136) *1/6= 20

3rd Attempt:

D = (256-156)*1/4= 25

At this point work remaining for M is 75 out of 256 . Hence 75/256 is answer

ScottTargetTestPrep · Answer

The best way to solve this problem is to keep track of the fraction of the barn that still needs to be completed after each of their shifts:

Dwight’s 1st shift: 1/4 → Fraction of the barn still needs to be completed: 3/4

Mose’s 1st shift: 1/6(3/4) = 1/8 → Fraction of the barn still needs to be completed: 5/6(3/4) = 5/8

Dwight’s 2nd shift: 1/4(5/8) = 5/32 → Fraction of the barn still needs to be completed: 3/4(5/8) = 15/32

Mose’s 2nd shift: 1/6(15/32) = 5/64 → Fraction of the barn still needs to be completed: 5/6(15/32) = 25/64

Dwight’s 3rd shift: 1/4(25/64) = 25/256 → Fraction of the barn still needs to be completed: 3/4(25/64) = 75/256

We can see that before Mose begins his 3rd shift, 75/256 of the barn still needs to be completed.

Answer: D

dcwanderer30 · Answer

I dont understand this pattern. Could you please clarify how you got to your solution step by step?

Fdambro294 · Answer

If (1/4) is taken away from the whole ——- (3/4) remains

If (1/6) is taken away from whatever is left——- (5/6) remains

D 1st shift: 3/4 remains

M 1st shift: (5/6) (3/4) remains

D 2nd shift: (3/4) (5/6) (3/4) remains

M 2nd shift: (5/6) (3/4) (5/6) (3/4) remains

D 3rd shift: (3/4)^3 * (5/6)^2 remains for Moses beginning his 3rd shift

(3 * 3 * 3 * 5 * 5)
______________
(4 * 4 * 4 * 6 * 6)

Cancel two of the 3’s in the numerator

75 / 256

Posted from my mobile device

anirchat · Answer

I am not smart enough to assume 256 units (kudos to the answer though, really intuitive), instead let us try to solve this with simple logic.

Work left = 
3/4 - After Dwight's first shift
5/6*3/4 - After Mose's first shift
3/4*5/6*3/4 - After Dwight's second shift
5/6*3/4*5/6*3/4 - After Mose's second shift
3/4*5/6*3/4*5/6*3/4 -  After Dwight's third shift  or  before Mose's second shift  = 75/256

bumpbot · Answer

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Dwight and Mose decide to build a new barn on their farm, and they beg

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