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

[BTGmoderatorDC]

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

[fskilnik@GMATH]

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

$$?\,\,:\,\,{\rm{remaining}}\,\,\left( {{\rm{fraction}}} \right)\,\,{\rm{job}}\,\,{\rm{before}}\,\,{\rm{Mose}}\,\,{\rm{third}}\,\,{\rm{shift}}$$
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.

Regards,
Fabio.

[Jay@ManhattanReview]

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 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.

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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[kyuhunl]

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

3/4 * 5/6 * 3/4 * 5/6 * 3/4 = 75/256