What percent of a data set is represented in quartile 1?

You need to understand the meaning of "quartile."  Finding the 1st, 2nd, 3rd and 4th quartiles, we essentially divide the data set into four sets, maintaining the order in which the data was presented.  Dividing into four sets is similar to drawing three vertical lines through the data to divide the set into four subsets.

The first set (beginning on the left) is the first quartile, and contains 25% of the data.  The next quartile contains 25%, the third, 25%, and the fourth 25%.