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If the productivity of a brigade grows by 10% when the numbe

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Director
Joined: 09 Aug 2006
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If the productivity of a brigade grows by 10% when the numbe  [#permalink]

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07 Jan 2008, 09:14
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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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Re: The productivity of a brigade grows by 10% when the number  [#permalink]

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16 May 2013, 08:42
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Stiv wrote:
This is the question from GMATClub test. The explanation from the solution of the question is excellent, but I want to know is there more than one way to solve this question.

On the GMATClub test the explanation is next:
p = increase in the productivity = 10%

Solution: B x p = B x 1.1 = 1.1B -------> the productivity of 11 men brigade
1.1B x p = 1.1B x 1.1 = 1.21B -----> the productivity of 12 men brigade

The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.21B/B = 1.21

In percentages, you can assume a value of 100. It simplifies the thought process.

If you increase the brigade by 1 worker, productivity grows by 10%. So say initial productivity is 100. If one more worker joins, productivity will be 110. If one more joins it will be 121 etc.
Ratio of productivity of 12 person to 10 person must be 121/100 = 1.21 (whenever there is a difference of 2 in the number of people, the ratio of productivity will be 1.21 assuming positive number of people)

Also, this is a successive percentage increase so you can use the formula: a + b + ab/100 = 10 + 10 + 10*10/100 = 21% increase.
Hence the required ratio is 121/100 = 1.21
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Re: PS: Ratio of Productivity  [#permalink]

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07 Jan 2008, 09:20
1
It's like compound interest.

Growth of 10% from 10 is indeed 1, to 11.
But growth of 10% from 11 is indeed 1.1, to 12.1.
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Re: PS: Ratio of Productivity  [#permalink]

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07 Jan 2008, 09:28
GK_Gmat wrote:
The productivity of a brigade grows by 10% when the number of the workers in the brigade is increased by one. Which of the following is closest to the ratio of the productivity of a 12-men brigade to that of a 10-men brigade?
0.21
0.82
1.20
1.21
1.44

Can someone please explain why C is wrong? Thanks.

I agree with raffie, C is wrong because 1.2 is ratio if each 10% is added to the tenth worker rather than eleventh which is wrong, twelves man adds 10% to the total 11 workers
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Re: PS: Ratio of Productivity  [#permalink]

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07 Jan 2008, 10:21
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The most powerful force in the universe is compound interest - Albert Einstein
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Re: PS: Ratio of Productivity  [#permalink]

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07 Jan 2008, 19:19
2
1
GK_Gmat wrote:
The productivity of a brigade grows by 10% when the number of the workers in the brigade is increased by one. Which of the following is closest to the ratio of the productivity of a 12-men brigade to that of a 10-men brigade?
0.21
0.82
1.20
1.21
1.44

Can someone please explain why C is wrong? Thanks.

D,
productivity of a 10-men brigade assumed is 10
when added 1 man, it is increasing by 10*1.1 =11
when added 1 more, it s increasing by 11*1.1 =12.1= productivity of a 12-men brigade
so, the ratio=12.1/10 =1.21
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Re: The productivity of a brigade grows by 10% when the number  [#permalink]

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15 May 2013, 22:53
This is the question from GMATClub test. The explanation from the solution of the question is excellent, but I want to know is there more than one way to solve this question.

On the GMATClub test the explanation is next:
p = increase in the productivity = 10%

Solution: B x p = B x 1.1 = 1.1B -------> the productivity of 11 men brigade
1.1B x p = 1.1B x 1.1 = 1.21B -----> the productivity of 12 men brigade

The ratio of the productivity of a 12-men brigade to that of a 10-men brigade = 1.21B/B = 1.21
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Re: If the productivity of a brigade grows by 10% when the numbe  [#permalink]

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17 May 2013, 00:51
Thank you, that is very helpful! It's important to remember new ideas about solving a problem...
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Re: Best or Worste Word Problem  [#permalink]

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20 May 2013, 14:27
$$\frac{P_{12}}{P{10}}=?$$

$$P_{12}=P{10}+2$$ each person inrease the prod by 10% so 2 people increase the prod by (1+10%)*(1+10%)=1.21

$$\frac{1.21P_{10}}{P{10}}=1.21$$

D

hope it's clear let me know
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Re: Best or Worste Word Problem  [#permalink]

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20 May 2013, 14:27
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

As the OA mentions, the answer is [D].

Let the total number of workers be x in the brigade and the corresponding productivity be p.
Now as per the question, if the worker number increases to x + 1 the final productivity is 110*p/100 ****10% rise in productivity.
Now further applied, if the number further increases by 1 i.e. x+2, the final productivity would be 110*110*p/100*100 => 121*p/100

Hence, when the ratio is taken between the productivity of x+2 and x workers, the value is 121/100 i.e 1.21. ****since its generalized, if x = 8, x+2 =10.

Hope the above explains your queries over the question!

Regards,
Arpan
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Re: If the productivity of a brigade grows by 10% when the numbe  [#permalink]

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20 May 2013, 15:11
New Productivity after 1 worker is increased = 1+10/100 = 1.1
Cascaded Increase = 1.1 * 1.1 ....
=> Productivity Increase for 12 (1.1)^12
--------------------------------- = ------------ = (1.1)^2 = 1.21
Productivity Increase for 10 (1.1)^10

Hence IMO (D)
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Re: If the productivity of a brigade grows by 10% when the numbe  [#permalink]

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01 Jul 2019, 17:20
GK_Gmat wrote:
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

We can let a 10-person brigade’s productivity be 100; thus, a 11-person brigade’s productivity will be 100 x 1.1 = 110, and a 12-person brigade’s productivity will be 110 x 1.1 = 121. Therefore, the ratio is 121/100 = 1.21.

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Re: If the productivity of a brigade grows by 10% when the numbe   [#permalink] 01 Jul 2019, 17:20
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