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Problem 545

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

Which of the following numbers is less than $\frac{1}{20}$ ?
(A) $\frac{1}{15}$
(B) $\frac{1}{25}$
(C) 0.5
(D) 0.055
(E) $\frac{1}{10}$

Your answer

Official solution

If $0\frac{1}{20}$ . Therefore, $\frac{1}{15}>\frac{1}{20}$ and $\frac{1}{10}>\frac{1}{20}$ .

Also, $\frac{1}{20}=0.05$ which is less than both 0.5 and 0.055 .

Lastly, $\frac{1}{20}>\frac{1}{25}$ since $0<20<25$ .

Therefore, $\frac{1}{25}$ is the only one of the choices that is less than $\frac{1}{20}$ .

ANswer: (B)

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.