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
OA D
Source: Veritas Prep
Dwight and Mose decide to build a new barn on their farm, an
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$$?\,\,:\,\,{\rm{remaining}}\,\,\left( {{\rm{fraction}}} \right)\,\,{\rm{job}}\,\,{\rm{before}}\,\,{\rm{Mose}}\,\,{\rm{third}}\,\,{\rm{shift}}$$BTGmoderatorDC 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
Source: Veritas Prep
Dwight 1st shift = (3/4) Job remaining.
Mose 1st shift = (5/6)*(3/4) Job remaining.
Dwight 2nd shift = (3/4)*(5/6)*(3/4) Job remaining.
Mose 2nd shift = (5/6)*(3/4)*(5/6)*(3/4) Job remaining.
Dwight 3rd shift = FOCUS = (3/4) *(5/6)*(3/4)*(5/6)*(3/4) Job remaining.
$${\rm{?}}\,\,{\rm{ = }}\,\,{3 \over 4} \cdot {5 \over 6} \cdot {3 \over 4} \cdot {5 \over 6} \cdot {3 \over 4}\,\, = \,\,{1 \over 4} \cdot {5 \over 2} \cdot {1 \over 4} \cdot {5 \over 2} \cdot {3 \over 4} = {{25 \cdot 3} \over {{4^4}}} = {{75} \over {256}}$$
We follow the notations and rationale taught in the GMATH method.
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Fabio.
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- Jay@ManhattanReview
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Since the question asks for the work left when Mose begins his third shift, Dwight must have done three and Mose must have done two shift.BTGmoderatorDC 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
OA D
Source: Veritas Prep
Since we will have to deal with 1/4 three times and 1/6 two times, for the ease of calculation, let's assume that total work = (4^3)*(6^2) = 2304
1. Work done by Dwight in I shift = 1/4 of 2304 = 576;
2. Work left = [(4^3)*(6^2)] - 576 = 2304 - 576 = 1728;
3. Work done by Mose in I shift = 1/6 of 1728 = 288;
4. Work left = 1728 - 288 = 1440;
5. Work done by Dwight in II shift = 1/4 of 1440 = 360;
6. Work left = 1440 - 360 = 1080;
7. Work done by Mose in II shift = 1/6 of 1080 = 180;
8. Work left = 1080 - 180 = 900;
9. Work done by Dwight in III shift = 1/4 of 900 = 225;
10. Work left = 900 - 225 = 675
Part of work left to finish when Mose begins his third shift = 675/2304 = 225/768 = 75/256
The correct answer: D
Hope this helps!
-Jay
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3/4 * 5/6 * 3/4 * 5/6 * 3/4 = 75/256BTGmoderatorDC 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
OA D
Source: Veritas Prep