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# M28-20

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Math Expert
Joined: 02 Sep 2009
Posts: 50652

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16 Sep 2014, 00:29
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Difficulty:

25% (medium)

Question Stats:

76% (00:46) correct 24% (01:27) wrong based on 159 sessions

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If the productivity of a brigade grows by 10% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?

A. 0.21
B. 0.82
C. 1.20
D. 1.21
E. 1.44

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Joined: 02 Sep 2009
Posts: 50652

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16 Sep 2014, 00:29
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Official Solution:

If the productivity of a brigade grows by 10% when the number of the workers in the brigade is increased by one, then which of the following is closest to the ratio of the productivity of a 12-person brigade to that of a 10-person brigade?

A. 0.21
B. 0.82
C. 1.20
D. 1.21
E. 1.44

If $$x$$ is the productivity of the 10-person brigade, the productivity of the 12-person brigade is $$1.1*1.1*x = 1.21*x$$. The required ratio $$= \frac{1.21x}{x} = 1.21$$.

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Joined: 05 Jun 2017
Posts: 7
Location: India
GPA: 3.67
WE: Science (Non-Profit and Government)

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21 Nov 2017, 23:39
2
my method is product change method

let initial value is 100
then 10% increase makes 110. further 10 % increase makes 121

now ratio of 121/100: 1.21
Intern
Joined: 12 Jan 2018
Posts: 19

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14 Jun 2018, 21:22
I have a question here -- I understand how the answer key derives its answer as the 10% compounds with the second additional worker (which is why it is 10 -> 11 -> 12.1 vs 10 = 12.1/10 = 1.21), but can't the productivity have compounded from the second worker, meaning the difference between the 10th and the 12th would be much higher? The question does not seem to imply that the brigade only begins the 10% increase starting with the tenth worker, it just specifies for each additional worker?

Interested to hear thoughts. Thanks!
Manager
Joined: 21 Jun 2017
Posts: 140
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)

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05 Nov 2018, 07:38
landoro15 wrote:
I have a question here -- I understand how the answer key derives its answer as the 10% compounds with the second additional worker (which is why it is 10 -> 11 -> 12.1 vs 10 = 12.1/10 = 1.21), but can't the productivity have compounded from the second worker, meaning the difference between the 10th and the 12th would be much higher? The question does not seem to imply that the brigade only begins the 10% increase starting with the tenth worker, it just specifies for each additional worker?

Interested to hear thoughts. Thanks!

TBH, Addition of one labor hardly makes any difference in productivity. This is a figurative question and not literal in any sense.
IF what you were thinking was considered , there can be infinitely many more reasons for increase/decrease in productivity.
What i am trying to say is labor is not linear to productivity. Only operating profit is.

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Joined: 28 Apr 2018
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07 Nov 2018, 13:51
Let' take as our base "10-person brigade" with a productivity of , say, x%. Given that for every single addition of one worker to the group the productivity increases by 10%, then
(10 + 1)11- person brigade = (x +0.1x)% =1.1x%
(10 +1 + 1)12- person brigade = (1.1x +0.1*1.1x)% = 1.21x%
Hence the ratio of 12- person brigade to 10-person brigade is 1.21x% : x% or 1.21 : 1 which makes our answer D .
Re: M28-20 &nbs [#permalink] 07 Nov 2018, 13:51
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# M28-20

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