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Bilingual Population

Expert replies
by moonstone1012001 » Fri May 08, 2009 7:45 am
Hi everyone, so I'm terrible at the Quant section of the GMATS so I apologize in advance if this is embarassing!!
:oops:

Here it is:

Are at least 20% of the people in City H who are at least 30 yrs old, Bilingual?

1. In City H, 30% of the pop is at least 30yrs old

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

(correct answer is B)

I chose B but my logic was wrong. :( I said that if you combine 18 + 17 than yes the pop >30 is bilingual. According to the answer, you can't combine male and female percentages. Why?? They are both part of the total population?

Any help is greatly appreciated!!!
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Source: — Data Sufficiency |

by DanaJ » Fri May 08, 2009 10:45 am
1 is insufficient because there's no reference to being bilingual or not.

2. Let's analyze this one: you are wrong in adding up those percentages. You're not talking about percentages of total population, you're talking about percentages of the female vs. male population.
Consider an example: a town has 500 men and 400 women. 300 men are over 30 years old, meaning that 60% of men are over 30 years old. 200 women are over 30 years old, meaning that 50% of women are over 30 years old. Combine these percentages to get well over 100%, which is obviously incorrect.

The point I'm trying to make is that the given percentages are not about total population: they each refer to the specific gender.

So you get that 18% of women over 30 are bilingual and 17% of men over 30 are bilingual. As you can see, both percentages are under 20%. This is why the answer to the initial question will be no, 20% of the population over 30 is NOT bilingual. Think of it this way: the percentage of people over 30 that are bilingual is going to be a weighted average of the percentages of women and men (respectively) over 30 who are bilingual. Depending on the number of women vs. the number of men, the average will be closer to 17 or to 18, but it will surely be somewhere in the middle.

Take my initial example: what will be the percentage of people over 30 in that town of 900? You have 500 people over 30 in a town of 900, or a percentage of 55%. As you can see, that percentage is somewhere between 50% and 60%.
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