Arithmetic

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Mon Sep 28, 2015 4:58 pm

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?

5/11

6/11

7/11

8/11

9/11

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Source: Beat The GMAT — Problem Solving | Mon Sep 28, 2015 4:58 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Sep 28, 2015 5:19 pm

sud21 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?

5/11

6/11

7/11

8/11

9/11

Let W = a day of work and R = a day of rest.
When Dale works at full efficiency, he requires a day of rest after every 2 days of work.
Thus, the 11 days look as follows:
WWRWWRWWRWW.
Implication of the 8 W's in red:
At full efficiency, Dale requires 8 days to complete the task.

Since Dale requires 11 days at reduced efficiency, the time ratio is as follows:
(reduced efficiency time)/(full efficiency time) = 11/8.
Since time and rate are RECIPROCALS, the rate ratio is equal to the reciprocal of the time ratio:
(reduced efficiency rate)/(full efficiency rate) = 8/11.

The correct answer is D.

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Mon Sep 28, 2015 5:30 pm

sud21 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?

5/11

6/11

7/11

8/11

9/11

At full efficency,
he works 2 days then take 1 day break,
he then work 2 days then take 1 day break,
he then work 2 days then take 1 day break,
he then work 2 days.
Therefore he work 8 days. His work rate is 1job/8days

At reduced efficency,
he works 11 days. His work rate is 1job/11days

Dale's output at reduced efficiency / output at full efficiency
= (1job/11days) / (1job/8days)
= (1job/11days) x (8days/1job)
= 8/11

ans = d

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by Scott@TargetTestPrep » Sun Dec 03, 2017 5:48 pm

sud21 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?

5/11

6/11

7/11

8/11

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

Answer: D

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by [email protected] » Sun Dec 03, 2017 7:27 pm

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.

Final Answer: D

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Rich

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