2007 Cyprus MO/Lyceum/Problem 5

Problem

If the remainder of the division of $a$ with $35$ is $23$ , then the remainder of the division of $a$ with $7$ is

$\mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 3\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } 5$

$\displaystyle a \equiv 23 \pmod{35}$ and $\displaystyle 7 | 35$ , so $\displaystyle a \equiv 23 \equiv 2 \pmod{7} \Longrightarrow \mathrm{B}$ .