Explanation

This is a rate question. In such questions, you should expect that nothing too fancy is going on here. All the rates can be expressed in a fraction measured in the right units, which in this case are molecules per minute (which means molecules over minutes). If we need to add them, subtract them, or compare them, we'll do so in that format. It turns out that the question is getting tricky with us by making ratios of ratios. The little p's are fractions that have the big P's in them. Glancing at the data statements, we see they are expressed in terms of the little p's, but we can apply the definition and substitute in the big P's, since that is what the question is really asking us about. So let's go do that, analyzing the statements separately first, as always.

Statement (1): if we substitute in what the little p's stand for, we get



The question is whether this factoid presented by Statement (1) means that is the greatest of the big P's. My hunch is no, since there are number of variables to play with, which indicates that we are likely to come up with cases yielding differing outcomes. Since these rates are all positive, the ratio is the same as



In one case, if were 1 and were largish, then could be smaller than that expression there and still be larger than However, in other case, could be largish, in which case the right side of the inequality is smallish, and is smaller than that, so it's not the largest. We don't have sufficient information from this statement to answer the question that has been posed.

Statement (2): here, we can start in the same way by substituting the little p's. Then we get,



This is useful, in that it tells us that is larger than . But we know nothing about , which could be big or small. So this statement also is insufficient.

Combining the statements, we have a common element in the two inequalities, allowing us to chain them together:



And since the leftmost term is smaller than another thing that is smaller than 1, the leftmost term is smaller than 1. So



So, now we know that is larger than . And is larger than by Statement (2); we have imported that fact into the combined case. So is the largest, definitively. We have sufficient information to answer the question.

The correct answer is (C).