GMAT Club invites you to test your GRE knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GRE Strategy guide. Tell your friends to get out their scrap paper and start solving! Click here to view contest & prize details This week's question: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%
Please post your answer, along with the explanation, below. Get cracking! Edit: Thank you for participating. The correct answer, and the winner will be announced shortly.
Solution
Problems that require us to synthesize information from two different charts or graphs and to answer a “which is closest”-type question can usually be answered most efficiently with a bit of estimating.
Looking at the pie chart, we see that people age 35-44 are 21% of the total and that people age 55-64 are 11% of the total. In other words, there are about twice as many 35-44’s as 55-64’s (since the whole problem is about just these two age groups, let’s just call them “younger” and “older” to make it easier to think about).
However, we are only interested in the employed people.
According to the bar graph, that’s 90% of the younger people and 40% of the older people. Thus:
21% of everyone is younger and 90% of them are employed. Therefore, about 18% of everyone is a younger person who is employed.
Similarly, 11% of everyone is older and 40% of them are employed. Therefore, about 4% of everyone is an older person who is employed.
Thus, employed younger people and employed older people exist in an 18 : 4 (or 9 : 2) ratio.
We know that the rate of volunteering among the younger people is three times as high as that among the older people.
Imagine for a moment that the younger and older people volunteered at the same rate. Since employed younger people and employed older people exist in an 9 : 2 ratio, then for every 900 employed younger people who volunteer, there would be 200 older people who volunteer.
But, actually, the rate for the older people is only 1/3 of that for the younger people. So, if 900 employed younger people volunteer, 1/3 of 200 older employed people volunteer. This is about 66.
So, about 66 employed older people volunteer. If 65 new older employed people decided to volunteer in 2009, the new number would about double the 2008 number, which is an increase of about 100%.
Note that the answer choices are far enough apart that, even if you estimated a bit differently, you would still get an answer that is clearly closest to 100%.
Want a recap?
• There are two groups in question, the younger and the older. The younger is about 20% of the total and the older is about 10% of the total.
• The younger group is also 90% employed while the older group is 40% employed.
• Thus, 90% of 20%, or 18%, is younger employed people, and 40% of 10%, or 4%, is older employed people.
• The 18% group volunteers at a three times higher rate than the 4% group, but we don’t know the rate.
• Whatever the rate is, it amounts to 900 people (those 900 are a subgroup of the 18% of everyone that is younger employed people).
• If the younger and older people volunteered at the same rate, then, since 18% and 4% make a 9 to 2 ratio, for every 900 younger volunteers, there’d be 200 older ones.
• But older people actually only volunteer at a third of that rate, and 1/3 of 200 is 66.6.
• If about 66 volunteered in 2008 and about that many join them in 2009, the group doubled.
The correct answer is E.
The winner of this Week's Challenge is... (drum roll).... DevilDoggNC. Congratulations! Please send me a pm with your shipping address, and choice of Manhattan GRE Guide
Details of next week's competition will be posted in the
Weekly Challenge Master thread... Stay tuned!
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