Data Sufficiency

himu wrote:Are at least 10 percent of the people in Country X who are 65 years old or older employed?

(1) In country X, 11.3 percent of the population is 65 year old or older
(2) In country X, of the population 65 year old or older, 20 percent of the men and 10 percent of the women are employed

(1) There is no information of the people employed. So, (1) is NOT SUFFICIENT.

(2) Now, the problem can be viewed as an weighted average problem.
20% of the men + 10% of women are employed. Although the number of men and women are not known, but the employment should be greater than 10% and less than 20%. So, (2) is SUFFICIENT.

The correct answer is B.

himu wrote:Are at least 10 percent of the people in Country X who are 65 years old or older employed?

(1) In country X, 11.3 percent of the population is 65 year old or older
(2) In country X, of the population 65 year old or older, 20 percent of the men and 10 percent of the women are employed

We need to determine whether at least 10 percent of the people in Country X who are 65 years old or older are employed. Let's refer to the population of those who are 65 years old or older in Country X as the "older population."

Statement One Alone:

In Country X, 11.3 percent of the population is 65 years old or older.

Knowing the percentage of the population in Country X who are 65 years old or older doesn't give us enough information to determine the percentage of the older population who are employed. For example, it could be the case that 5% of the older population are employed or it could be the case that 35% of them are employed. Statement one alone is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

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

Of the older population, if 20% of the men and 10% of the women are employed, then it must be true that the overall employment percentage is between 10 and 20 percent. Anytime there is a group of people or objects divided into two subgroups, if x percent of one subgroup satisfies a criterion and y percent of the other subgroup satisfies the same criterion, then the percentage of the whole group satisfying this criterion is some number between x and y percent. Since the percentage of the older population who are employed is between 10 and 20 percent, then at least 10 percent of them are employed. Statement two alone is sufficient.

Answer: B

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

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

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

Let's use the term seniors, to refer to those who are 65 years old or older.

Target question: Are at least 10 percent of Country X's seniors employed?

Statement 1: In Country X, 11.3 percent of the population is 65 years old or older.
Okay, so we know that a certain percent of the population are seniors, but we aren't told anything about their employment rates.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Among Country X's seniors, 20 percent of the men and 10 percent of the women are employed
To get a feel for what this tells us, let's examine the two EXTREMES:
Extreme #1 - among the seniors, there are ZERO women. This means all of the seniors are men, which means 20% of the seniors are employed
Extreme #2 - among the seniors, there are ZERO men. This means all of the seniors are women, which means 10% of the seniors are employed
Now that we have examined the extremes, we have a range of values that represent the employment rate among Country X's seniors.
We can conclude: 10% < senior employment rate < 20%
In other words, at least 10 percent of Country X's seniors are employed
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

By the way, this concept (and others) is covered in the following video on weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent