AHSME 1974 Problem 28

Which of the following is satisfied by all numbers $x$ of the form $$x=\frac{a_1}{3}+\frac{a_2}{3^2}+\cdots+\frac{a_{25}}{3^{25}}$$ where $a_1$ is $0$ or $2$, $a_2$ is $0$ or $2$,...,$a_{25}$ is $0$ or $2$? $\mathrm{(A)\ } 0\le x<1/3 \mathrm{(B) \ } 1/3\le x<2/3 \mathrm{(C) \ } 2/3\le x<1$ $\mathrm{(D) \ } 0\le x<1/3 \text{ or }2/3\le x<1 \mathrm{(E) \ }1/2\le x\le 3/4$