Answer
Cost: quantitative, continuous. It is measured at the ratio level.
Year: quantitative, discrete.
Work Step by Step
The cost is a quantitative continuous variable because there are infinite numbers we can use to measure cost. In other words, between two possible numbers, there are an infinite number of other possible numbers. Also, the ratio of two values makes sense and a value of zero has meaning (in this case, it means someone will study for free).
Year a quantitative discrete variable because we can count the years: 1, 2, 3,..., 1998, 1999, 2000, 2001, .... Also, the differences between years have meaning, that is is someone joined the college in 2005 and left in 2009, it means he or she stayed for 4 years in college. The year 2000 is not the double of the year 1000 and the year 1 is not the beginning of the world.
