A box plot shows a first quartile of 15 and a third quartile of 35. What is the interquartile range?

The interquartile range is the distance between the third and first quartiles: $\text{IQR}=Q_3-Q_1=35-15=20$, choice B. It measures the spread of the middle half of the data. Choice D ($50$) adds the two quartiles instead of subtracting them. Choice A ($15$) is the first quartile and choice C ($35$) is the third quartile; these are positions in the data, not the spread between them. The interquartile range is a width, so it should be smaller than the third quartile itself, which rules out choices C and D.