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2007 Cyprus MO/Lyceum/Problem 5

From AoPSWiki

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

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2007_Cyprus_MO/Lyceum/Problem_5"

Category: Introductory Algebra Problems

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