swerve 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. 75/26
E. 255/512
The OA is D
Source: Veritas Prep
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
