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Among people who count as full-time employed in Town X in 20

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Among people who count as full-time employed in Town X in 20 [#permalink] New post 22 Mar 2018, 12:23
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Among people who count as full-time employed in Town X in 2008, the rate of volunteering among full-time employed people age 35-44 is three times as high as it is among full-time employed people ages 55-64. If 900 full-time employed people ages 35-44 volunteer in 2008, and then 65 new people ages 55-64 begin to volunteer in 2009, which of the following would be closest to the percent increase from 2008 to 2009 in full-time employed people ages 55-64 who volunteer?

A. 19%

B. 27%

C. 42%

D. 65%

E. 100%
[Reveal] Spoiler: OA

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Re: Among people who count as full-time employed in Town X in 20 [#permalink] New post 23 Mar 2018, 02:11
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Let \(a\) be the total number of people in town x in 2008
From the pie chart:
total number of people in the 55-64 age category would be \(0.11a\)
total number of people in the 35-44 age category would be \(0.21a\)

From the bar graph:
Find the total number of employed people within the age group
Hence total number of employed worker in 55-64 category would be \(0.4 * 0.11 a = 0.044 a\)
Similary total number of employed worker in the 35-44 category would be \(0.9 * 0.21 a = 0.189 a\)

Now, Use the information in the question to formulate a equation
\(\frac{900}{0.189 a} = 3 * \frac{n}{0.044 a}\) [n is the total number of volunteer worker in the age group 55-64]
cross multiply to get the value of \(n = 70\)approx [a cancels out during division]
The question mentions that there is an increase of 65 volunteer workers over 2009 within the age group 55-64
Hence \(%\) increase in volunteer workers \(= \frac{(70+65) - 70}{70} * 100 = 92.8\)
This value is closest to option E
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Re: Among people who count as full-time employed in Town X in 20 [#permalink] New post 23 Mar 2018, 16:56
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This problem is pretty tough. We can certainly solve it using algebra but that seems a bit complex. Instead, first, let's find out what percent of people are both in the relevant age group and fully employed, for both age groups. Those aged 35-44 are 21% of the total population, and of this group, 90% are fully employed. If we round to 20% and multiply, we find that 20%x90% = 18%. Similarly, for those aged 55-64, representing 11% of the population, which we can round to 10%, and multiplied by the 40% that are fully employed, we find that fully employed 55-64 year-olds represent 10%x40% = 4% of the total population. So we have a ratio of 18:4, or 9:2, younger to older people.

We've also been told that the younger group produced 900 volunteers, so since the ratio is 9:2, we would expect the older group to produce 200 volunteers. However, we also know that the younger group volunteered 3 times more than the older group, so if we divide 200 by 3, we find that the older group produced about 67 volunteers.

Thus, if in 2009, 65 new older people began volunteering, we can say that they increased by about 100%, giving us an answer of E.
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Re: Among people who count as full-time employed in Town X in 20 [#permalink] New post 09 Sep 2018, 15:27
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It says age 35-44 is three times as high as it is among full-time employed people ages 55-64. I automatically assumed that if 900 are volunteering for 35-44 age group then 300 are volunteering for 55-64 age group. SO when 65 gets added, percent increase is (65/300)*100=21%. I chose A, because 19% was the closest. I now know it is not right but I still don't understand how and why? can you explain why did you do this step:
900/0.189a=3∗(n/0.044a).
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Re: Among people who count as full-time employed in Town X in 20 [#permalink] New post 10 Sep 2018, 07:42
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It is the rate of percent which is 3 times not the actual number. We have the figure of volunteers for 35-44 age group which is 900. But to find the number of volunteers for 55-64 age group we have to form a equation based on % hence for this reason the aforementioned step was done.
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