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RATIO

by quitaskinme » Sat Oct 31, 2015 11:26 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?

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

Here is the solution:
My question is how does 1/11:1/8 get reduced to 8/11? Doesn't the : mean they are multiplied??

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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by theCEO » Sun Nov 01, 2015 2:29 am
quitaskinme 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

Here is the solution:
My question is how does 1/11:1/8 get reduced to 8/11? Doesn't the : mean they are multiplied??
.
the : mean they are divided; (1/11) / (1/8) = 8/11

Here is an alternative way to solve:
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 GMATGuruNY » Sun Nov 01, 2015 3:34 am
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.
My question is how does 1/11:1/8 get reduced to 8/11? Doesn't the : mean they are multiplied??
To divide by one fraction by another, we multiply the top fraction by the RECIPROCAL of the bottom fraction:
(1/11) / (1/8) = (1/11)(8/1) = 8/11.
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by [email protected] » Sun Nov 01, 2015 11:06 am
Hi quitaskinme,

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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