In a country with a working-age population of 20 million, 13 million are employed, 1.5 million are unemployed, and 1 million of the employed are...

This question is meant to determine whether you know what the labor force is and whether you can filter out extraneous information presented to you in a question.  Once you understand both of these things, you will find that the labor force in this country consists of 14.5 million people.

In economic terms, the labor force of a country consists of those people who are willing and physically able to work in paid jobs.  What...

This question is meant to determine whether you know what the labor force is and whether you can filter out extraneous information presented to you in a question.  Once you understand both of these things, you will find that the labor force in this country consists of 14.5 million people.

In economic terms, the labor force of a country consists of those people who are willing and physically able to work in paid jobs.  What this means is that the labor force includes people who have jobs (because they are clearly willing and able to work) and those who are unemployed (because the technical definition of unemployment includes only those people who are willing and able to work but who cannot find jobs).  The people who are not in the labor force include such groups as children who are too young to work and retirees who no longer wish to work.

With this definition in mind, let us look at what information in the question is relevant.  The total population of the country is irrelevant because we are not looking for what percentage of the population is in the labor force.  All we are trying to do is find out the number of people in the labor force.  The fact that 1 million people are employed part-time, and that 500,000 of them do not get to work as much as they want, is irrelevant to this question.  Those people are employed and so they are part of the labor force, regardless of how long they work and whether they are happy with their hours.

This leaves us with two relevant numbers.  There are 13 million employed people and 1.5 million unemployed people.  Since the labor force is made up of those who are employed and those who are unemployed, the labor force in this country is 14.5 million people.