Explanation

To answer this question, we need to know either both defect rates, and , or an inequality that directly compares the two rates, in which case we'd know which is greater without knowing their actual values.Let's see what we get in the data statements, evaluating separately first.

Statement (1) compares defects, but not runs. That still permits wildly different cases. For example, the first run might have 10 times as many defects as the second run, but, for all we know, it could have a hundred times as many total items, or one-tenth as many items. In those cases the defect rates would compare different, so the information given in Statement (1) is insufficient.

Statement (2) has the same logical problem as Statement (1), as examining cases can show. Insufficient.

Combining the statements, there may be something that we can do. If there are more defects in the first run, but more items in the second run, then the first run must have a higher defect rate. We can see this by considering a limit condition. Say the two runs had the same number of total items (the r's are the same). Then, if the first run had higher defects, it has a higher defect rate: would be greater than . Then, if we make bigger, that only increase the difference, because it would increase the denominator of and make it smaller. The information we have establishes that the first run has a higher defect rate.

The correct answer is (C).