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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Jan 28, 2019 11:04 pm

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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

Source: Beat The GMAT — Problem Solving | Mon Jan 28, 2019 11:04 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Tue Jan 29, 2019 4:30 am

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

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

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Jan 29, 2019 10:34 pm

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 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: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Jan 29, 2019 3:16 am

by kyuhunl » Tue Jan 29, 2019 10:57 pm

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

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

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