Which is the largest sum?
(A) $\frac{1}{4}+\frac{1}{5}$
(B) $\frac{1}{4}+\frac{1}{6}$
(C) $\frac{1}{4}+\frac{1}{3}$
(D) $\frac{1}{4}+\frac{1}{8}$
(E) $\frac{1}{4}+\frac{1}{7}$
We first recognize that $\frac{1}{4}$ is a common fraction in each of the five sums, and so the relative size of the sums depends only on the other fractions.

Since $\frac{1}{3}$ is the largest of the fractions $\frac{1}{5}, \frac{1}{6}, \frac{1}{3}, \frac{1}{8}, \frac{1}{7}$, we conclude that $\frac{1}{4}+\frac{1}{3}$ is the ANSWER: (C)