Challenge Problem(DI)

[anup5889]

https://www.manhattanprep.com/gre/Chall ... chive/1168
How is it assumed that the younger employed volunteering people are 200?
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.
(How it is taken that the younger employed volunteering people are 200, is it given anywhere? )
• If about 66 volunteered in 2008 and about that many join them in 2009, the group doubled.

The correct answer is E.

[faedrus]

Read the explanation again. The only assumption made (given in the problem statement) is that 900 younger employed people volunteer. Since the ratio of younger employed to older employed is 9:2, then if we assume the younger employed and older employed volunteer at the same rate (they don't, but this will help us find the answer), that would mean there are Y older employed volunteers where 9/2 = 900/Y means Y = 200. The answer never assumes there are 200 younger employed volunteers. The 200 comes from an intermediate step to reach the number of older employed volunteers assuming they volunteer at the same rate as younger employed people.

To avoid confusion and finish the problem: the problem also states that the older employed volunteer at a rate that is 1/3 that of the younger employed volunteers (not at the same rate like we assumed above). Thus 200/3 = 66.6.

[tommywallach]

Yep, this has been explained perfectly by mbonakda. Well done!

-t