A5. Given a stack of boxes, it is stated that a quarter of the boxes are empty. We open a quarter of the boxes and see that one fifth of them are not empty.

What fraction of the unopened boxes is empty?
A) $\frac{4}{15}$
B) $\frac{1}{4}$
C) $\frac{1}{15}$
D) $\frac{1}{16}$
E) $\frac{1}{20}$
A5. C) $\frac{1}{15}$ For convenience, we can assume there are 20 boxes; this does not affect the ratios. Of the 20 boxes, 5 are empty. Of the 5 boxes that are opened, one fifth are not empty, exactly 1 box. Since 4 of the opened boxes are empty, there is exactly 1 empty box left among the 15 unopened boxes.