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

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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.

Answer: B

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Vincen wrote:
Thu Apr 15, 2021 11:37 am
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.

Answer: B

Source: GMAT Prep
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
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