Hi, there. I'm happy to explain this.

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

Statement #1: In Country X, 11.3 percent of the pop is 65 yrs old or older.
Statement #1 is does not help at all. It mentioned zilch about employment vs. unemployment, and does nothing to help us understand the make-up of the 65+ yo segment of the population. It's a useless as a one-legged man at a butt-kicking contest. Statement #1 is insufficient.

Statement #2: In Country X, of the pop 65 years old or older, 20% of the men and 10% of the women are employed.
This is interested, and get into an important fact about averages.

Suppose a group has members from just two categories, Type A and Type B. If the average of the Type A folks is N, and the average of the Type B folks is M, the average of the whole group is a weighted average. One could only calculate that weighted average if one knows the ratio --- how many A's vs. how many B's. Short of that, though --- suppose M < N, for the sake of argument. Then we know:

M < weighted average of whole group < N

In other words, we know the weighted average if the group must fall somewhere between the weighted averages of the two subsets.

Similarly, if a group has members from just two categories, Type A and Type B, and M% of the A's do something, and N% of the B's do that thing, where M < N, and P is the percent of the whole group who does that thing, we can say:

M < P < N

The percent of the whole group must be between the percents of the subgroups. Again, if we knew the exact proportion of A to B, we could figure out the exact percentage, but in the absence of that knowledge, this inequality always holds.

Thus, among the 65+yo crowd, if 20% of mean and 10% of women are employed, and these two subgroups (men & women) can reasonably be assumed to constitute the whole population*, then we know the percent of the 65+yo crowd must be greater than 10% and less than 20%. Thus, we are able to answer the prompt question. Statement #2 is sufficient.

Answer = B

*My apologies for the heteronormative assumptions of the foregoing analysis, which I understand could be deeply offensive to transgender & transsexual folks and their allies. I am deeply sympathetic to their cause. All I can say here is that, unfortunately, in GMAT problems where gender arises, the GMAT seems unrelentingly heteronormative, and thus the assumption is necessary to answer GMAT questions correctly. Of course, success in the business world in the 21st century will require considerably more sensitivity on this issue.

Does my explanation of the question make sense? Please let me know if you have any further questions.

Mike