Data Sufficiency

There are at least 10% of the people in Country X who are 65 years old or older employed?

1) In Country X, 11.3% of the population is 65 years old or older.

2) In Country X, of the population 65 years old or older, 20% of the men and 10% of the women are employed.

The OA is B does any one know how?

eyoussef wrote:There are at least 10% of the people in Country X who are 65 years old or older employed?

1) In Country X, 11.3% of the population is 65 years old or older.

2) In Country X, of the population 65 years old or older, 20% of the men and 10% of the women are employed.

The OA is B does any one know how?

Hi eyoussef,

1) is not sufficient--> no info about the employed.

2) The population of country X is comprised of men and women. You're given the percentage (20%) of employed men over 65 and that (10%) of employed women over 65.

Say Y is the percentage of employed people in Country X who are at least 65.
P is the number of of employed people in Country X who are at least 65.
M is the number of employed men who are at least 65.
W is the number of employed women who are at least 65.

Then Y%(P) = 20%M + 10%W with M + W = P

so Y% = (20%M + 10%W)/(M + W)

This weighted average formula will give you the value of Y in a problem solving question.

But we are in DS here, aren't we?

The arithmetic or weighted average must always fall somewhere between the lowest number and the greatest number in the list to be averaged.
I am sure you'll agree to that.

Therefore, Y must be between 10% and 20%.
Y must be at least 10% and is actually greater than 10% if there is a least one employed man over 65.

(B) is the correct answer.

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This was a GMAT math recipe from the GMAT chef.