City H (Percentage Question)

[MelissaLim]

Hi experts and all,

I still do not understand the answer explanation given for this question. Can someone kindly explain?

Source: Kaplan GMAT Premier Live Online 2010 Edition

Are at least 20 percent of the people in City H who are at least 30 years old bilingual?

1. In City H, 30 percent of the population is at least 30 years old.

2. In City H, of the population 30 years old or older, 18 percent of the women and 17 percent of the men are bilingual

OA:[spoiler]B. Why is it B? The answer choice explains that since neither group is at least 20 percent bilingual, the total population (women and men) of people 30 and over must be less than 20 percent bilingual. [/spoiler]

[Mike@Magoosh]

Hi, there. I'm happy to help with this.

That's a great question. The framework of the question leads us to think in terms of a double matrix solution, what do we know about the two categories, etc.

Instead, they threw you a curveball: the question is really about weighted averages.

Suppose I have a big set with made of type-A elements and type-B elements.

Of all the A elements, 56% have a certain quality. Of all the B elements, 35% have a certain quality. I want to know what percent of the whole set has that quality. Well, of course, since I don't know the relative proportion of A and B, I can't figure out the exact value, but I do know:

35 < percent of whole set < 56

It's the same as with averages. If you know the average of both subgroups, and the set contains only those two subgroups, then the average of the set has to be between the averages of the subgroups.

Here, the set of 30 years old or older in City H is made of just two subgroups: males and females.

18% of the women in the set are bilingual.
17% of the women in the set are bilingual.

That means:

17% < % of 30 yo in city H who are bilingual < 18%.

We know the number has to be between 17 and 18, which means that it's clearly less than 20%, which is why B is correct.

Does that make sense? Please let me know if you have any questions on what I've said.

Mike