Which of the following fractions is both larger than $\frac{1}{6}$ and smaller than $\frac{1}{4}$ ?
(A) $\frac{5}{12}$
(B) $\frac{5}{36}$
(C) $\frac{5}{24}$
(D) $\frac{5}{60}$
(E) $\frac{5}{48}$
We note that $\frac{1}{6}=\frac{5}{30}$ and that $\frac{1}{4}=\frac{5}{20}$.

If we compare two fractions with equal positive numerators, the fraction with the smaller positive denominator will be largest of the two fractions.

Therefore, $\frac{5}{30}<\frac{5}{24}$ and $\frac{5}{24}<\frac{5}{20}$, or $\frac{1}{6}<\frac{5}{24}<\frac{1}{4}$.

(Alternatively, we could note that since $\frac{1}{6}=\frac{6}{24}$ and that $\frac{1}{4}=\frac{6}{24}$, then $\frac{5}{24}$ must be the one of the given choices that is between these.)