Data Sufficiency

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 our free video on weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Cheers,
Brent

Hi eitijan,

While this IS a weighted average question, you don't actually have to do ANY calculations to solve it. In that way, it's a great "concept" question - if you recognize (and understand) the concept, then you can quickly answer the question (you do have to pay careful attention to all of the details though).

We're asked if AT LEAST 10% of the people who are 65 or older are employed. This is a YES/NO question.

Fact 1: 11.3% of the population is 65 or older.

This tells us NOTHING about whether these people are employed or not.
If 100% of them are employed, then the answer is YES.
If 0% of them are employed, then the answer is NO.
Fact 1 is INSUFFICIENT

Fact 2: Of those 65 years or older, 20% of the men and 10% of the women are employed.

Take a moment to think about the question that was asked. Are AT LEAST 10% of the people aged 65 or older employed? From this Fact, we know that there are some men and some women in this group. With 20% of the men and 10% of the women from this group employed, the weighted average MUST be between 10% and 20%, which means that the answer to the question is ALWAYS YES. The group is AT LEAST 10% employed; you don't have to do any math to prove it.
Fact 2 is SUFFICIENT.

Final Answer: B

It's worth noting that most DS questions require a lot more work than this question required, so you won't be able to "talk" your way past too many of them. If you really know your math rules/concepts/patterns though, you will be able to answer a few DS prompts on Test Day with a minimal amount of work.

GMAT assassins aren't born, they're made,
Rich

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.

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