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2007 Cyprus MO/Lyceum/Problem 5

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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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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