What is the total number of years when combining the 6 week CAD workshops and the Christmas CAD workshops?

What is the total number of years when combining the 6 week CAD workshops and the Christmas CAD workshops?

• A. 3
• B. 4
• C. 5
• D. 6

Answer: (C)

Think about how many different years show at least one CAD workshop. The trick is to count years, not workshop sessions. If you simply add up how many years host the six-week workshops and how many years host the Christmas workshops, you might double-count any year that has both types. To see why the five-year total makes sense, imagine the six-week workshops happen in three years and the Christmas workshops happen in four years. If two of those years overlap (both types happen in the same year), you subtract those overlapped years once: 3 + 4 − 2 = 5 distinct years with at least one workshop. That’s the quantity you’re asked for—the total number of years covered by both programs. If you didn’t account for overlap, you’d end up with more than five; if you assumed every year has both types, you’d get fewer. The counted value ends up being five distinct years.

Think about how many different years show at least one CAD workshop. The trick is to count years, not workshop sessions. If you simply add up how many years host the six-week workshops and how many years host the Christmas workshops, you might double-count any year that has both types.

To see why the five-year total makes sense, imagine the six-week workshops happen in three years and the Christmas workshops happen in four years. If two of those years overlap (both types happen in the same year), you subtract those overlapped years once: 3 + 4 − 2 = 5 distinct years with at least one workshop. That’s the quantity you’re asked for—the total number of years covered by both programs.

If you didn’t account for overlap, you’d end up with more than five; if you assumed every year has both types, you’d get fewer. The counted value ends up being five distinct years.