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

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

Solution

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

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 4
Followed by
Problem 6
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