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# If Dale works at full efficiency he needs a break of 1 day after every

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Math Expert
Joined: 02 Sep 2009
Posts: 45497
If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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21 Apr 2015, 06:03
1
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Difficulty:

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Question Stats:

82% (01:08) correct 18% (01:39) wrong based on 212 sessions

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If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A. 5/11
B. 6/11
C. 7/11
D. 8/11
E. 9/11

Kudos for a correct solution.

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Re: If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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21 Apr 2015, 06:26
1
KUDOS
Hi,
IMO it should be D 8/11.
though I am not very confident for this but still a feeble attempt.
Total working days were 8 days at original efficiency.
new efficiency were 11 days
so may be not a good approach even though answer might be of might not be correct.
8/11

Regards
Celestial

Kudos for a correct answer or even for trying as if it would have been in exam then there wasn't any way to escape it.

Bunuel wrote:
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A. 5/11
B. 6/11
C. 7/11
D. 8/11
E. 9/11

Kudos for a correct solution.
Senior Manager
Joined: 27 Dec 2013
Posts: 283
Re: If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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21 Apr 2015, 10:38
1
KUDOS
1
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IMO answer should be D- 11 days..

At full efficiency, he can finish the work in 8 days and at reduced efficiency he will complete the work in 11 days.

Hence 8/11

Bunuel wrote:
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A. 5/11
B. 6/11
C. 7/11
D. 8/11
E. 9/11

Kudos for a correct solution.

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Kudos to you, for helping me with some KUDOS.

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Re: If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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21 Apr 2015, 20:06
1
KUDOS
Expert's post
Hi All,

There's a visual 'component' to this question that will probably help you to solve it.

We're told that there are 2 ways for Dale to complete a job:

1) Full Efficiency: 2 days of work followed by 1 day "off" for a total of 11 days.
2) Reduced Efficiency: 11 straight days with no days off.

Working at Full Efficiency creates the following pattern:

2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2 = 11 days
Totals: 8 days on, 3 days off

Reduced Efficiency means that Dale will do 8 days of work in 11 days, thus those Reduced "days" are 8/11 of Full Efficiency.

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Re: If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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22 Apr 2015, 01:09
1
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One more for D
At full efficiency Dale works for 2+2+2+2 = 8 days, and 3 days rest.
At reduced efficiency Dale works for full 11 days.
Thus fraction = 8/11
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Posts: 45497
Re: If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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27 Apr 2015, 03:15
Bunuel wrote:
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A. 5/11
B. 6/11
C. 7/11
D. 8/11
E. 9/11

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

If Dale needs to rest every third day at full efficiency, that means he'll rest on days 3, 6, and 9 before finishing the job on day 11. That means that he'll have worked a total of 8 days, accomplishing 1/8 of the job each day.

At reduced efficiency, he works a total of 11 days, completing 1/11 of the job each day.

Therefore, the ratio of his output at reduced to his output at full is 1/11 : 1/8. That reduces to 8/11.
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Re: If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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03 Dec 2017, 18:47
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Expert's post
Bunuel wrote:
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A. 5/11
B. 6/11
C. 7/11
D. 8/11
E. 9/11

When Dale works at full efficiency, he actually works 8 days of the 11 days (notice that 2 + 1 + 2 + 1 + 2 + 1 + 2 = 11). When Dale works at reduced efficiency, he works 11 days.

If we let his output at reduced efficiency = r and his output at full efficiency = f, then we have:

11r = 8f

r/f = 8/11

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If Dale works at full efficiency he needs a break of 1 day after every [#permalink]

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05 Dec 2017, 14:39
Bunuel wrote:
If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 11 days. If he works at reduced efficiency, he can work without break and finish that same job in 11 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?

A. 5/11
B. 6/11
C. 7/11
D. 8/11
E. 9/11

Kudos for a correct solution.

I learned efficiency a bit differently, so this method was easier.

Full efficiency, X = one day's work:
X X _ X X _ X X _ X X = $$\frac{1Job}{8days}$$

Reduced efficiency:

X X X X X X X X X X X = $$\frac{1Job}{11days}$$

Reduced efficiency as fraction of full efficiency

$$\frac{(\frac{1}{11})}{(\frac{1}{8})}=\frac{1}{11}*\frac{8}{1}=\frac{8}{11}$$

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If Dale works at full efficiency he needs a break of 1 day after every   [#permalink] 05 Dec 2017, 14:39
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