The largest number in the list $\left\{\frac{3}{10}, \frac{9}{20}, \frac{12}{25}, \frac{27}{50}, \frac{49}{100}\right\}$ is
(A) $\frac{3}{10}$
(B) $\frac{9}{20}$
(C) $\frac{12}{25}$
(D) $\frac{27}{50}$
(E) $\frac{49}{100}$
Solution 1

To compare the five fractions we rewrite them each with a common denominator of 100 .

Then the list equivalent to the given list $\left\{\frac{3}{10}, \frac{9}{20}, \frac{12}{25}, \frac{27}{50}, \frac{49}{100}\right\}$ is $\left\{\frac{30}{100}, \frac{45}{100}, \frac{48}{100}, \frac{54}{100}, \frac{49}{100}\right\}$.

The largest number in this new list is $\frac{54}{100}$, and therefore $\frac{27}{50}$ is the largest number in the given list. Solution 2

We notice that with the exception of $\frac{27}{50}$, each numerator in the given list is less than one half of its corresponding denominator.

Thus, each fraction except $\frac{27}{50}$ has a value that is less than one half.

The fraction $\frac{27}{50}$ is larger than one half.

Therefore $\frac{27}{50}$ is the largest number in the list.

ANSWER: (D)