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4 men and 10 women were assigned to complete a work. Can they complete

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Bunuel
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4 men and 10 women were assigned to complete a work. Can they complete [#permalink] New post   05 Jul 2017, 00:45
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4 men and 10 women were assigned to complete a work. Can they complete the work within 15 days? Assume that all men are equally efficient and all women are equally efficient.

(1) 4 men and 10 women employed initially completed 1/3 of the work in less than 6 days.
(2) If 2 additional men and 2 additional women had been employed, they would have completed 1/2 of the work in 5 days (the additional men and the additional women have efficiencies equal to the men and women employed initially, respectively).
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Luckisnoexcuse
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Re: 4 men and 10 women were assigned to complete a work. Can they complete [#permalink] New post   05 Jul 2017, 01:31
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Bunuel wrote:
4 men and 10 women were assigned to complete a work. Can they complete the work within 15 days? Assume that all men are equally efficient and all women are equally efficient.

(1) 4 men and 10 women employed initially completed 1/3 of the work in less than 6 days.
(2) If 2 additional men and 2 additional women had been employed, they would have completed 1/2 of the work in 5 days (the additional men and the additional women
have efficiencies equal to the men and women employed initially, respectively).


4M & 10 W can complete the task within 15 days?

(1) says if 4 M & 10 W initially complete the 1/3 task in less than 6 days

if they completed in 3 days then they will finish total task in 9 days (within 15 days) but
if they completed the task in 5.5 days then they will finish the task in 16.5 days (beyond 15 days)

Hence Not sufficient

(2) if 4M+2M and 10W+2W are working they can finish 1/2 task in 5 days and hence the complete task in 10 days

so these 6M + 12W = 10 days
1M + 2W = 60 days
4 M + 8W = 15 days in question wee have 4M + 10W (they will finish the task before 15 days)
and hence Sufficient
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UNCalum8
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Re: 4 men and 10 women were assigned to complete a work. Can they complete [#permalink] New post   29 Jul 2020, 08:25
Luckisnoexcuse wrote:
Bunuel wrote:
4 men and 10 women were assigned to complete a work. Can they complete the work within 15 days? Assume that all men are equally efficient and all women are equally efficient.

(1) 4 men and 10 women employed initially completed 1/3 of the work in less than 6 days.
(2) If 2 additional men and 2 additional women had been employed, they would have completed 1/2 of the work in 5 days (the additional men and the additional women
have efficiencies equal to the men and women employed initially, respectively).


4M & 10 W can complete the task within 15 days?

(1) says if 4 M & 10 W initially complete the 1/3 task in less than 6 days

if they completed in 3 days then they will finish total task in 9 days (within 15 days) but
if they completed the task in 5.5 days then they will finish the task in 16.5 days (beyond 15 days)

Hence Not sufficient

(2) if 4M+2M and 10W+2W are working they can finish 1/2 task in 5 days and hence the complete task in 10 days

so these 6M + 12W = 10 days
1M + 2W = 60 days
4 M + 8W = 15 days in question wee have 4M + 10W (they will finish the task before 15 days)
and hence Sufficient
B


I'm a little confused how you get 4M + 2M from the work = rate * time equation, could anyone explain this. I want ot understand the logic behind it and not just memorize it, but I can't quite get there.
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Re: 4 men and 10 women were assigned to complete a work. Can they complete [#permalink] New post   09 Nov 2022, 07:51
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Bunuel wrote:
4 men and 10 women were assigned to complete a work. Can they complete the work within 15 days? Assume that all men are equally efficient and all women are equally efficient.

(1) 4 men and 10 women employed initially completed 1/3 of the work in less than 6 days.
(2) If 2 additional men and 2 additional women had been employed, they would have completed 1/2 of the work in 5 days (the additional men and the additional women have efficiencies equal to the men and women employed initially, respectively).


Solution:
Pre Analysis:
  • Work by 4 men in 15 days \(=nRT=4\times M\times 15=60M\) where M is the rate of each man
  • Work by 10 women in 15 days \(=nRT=10\times W\times 15=150W\) where W is the rate of each woman
  • We are asked if \(60M+150W=Work \) or not

Statement 1: 4 men and 10 women employed initially completed 1/3 of the work in less than 6 days
  • If they (4 men and 10 women) complete the 1/3 work in 5 days, then they will complete the work in \(5\times 3=15\) days
  • However, if they complete it in less than that, they won't be able to complete the full work in 15 days
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: If 2 additional men and 2 additional women had been employed, they would have completed 1/2 of the work in 5 days
  • Work by 6 men in 5 days \(=nRT=6\times M\times 5=30M\)
  • Work by 12 women in 5 days \(=nRT=12\times W\times 5=60W\)
  • According to the statement \(30M+60W=\frac{Work}{2}⇒60M+120W=Work\)
  • This means \(60M+150W=Work \) is not true and we can answer the question

Hence the right answer is Option B
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Re: 4 men and 10 women were assigned to complete a work. Can they complete [#permalink]
09 Nov 2022, 07:51
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Bunuel
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