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PrintSouth African Mathematics Olympiad First Round
South Africa number theory
Problem
In rugby it is possible to score 3, 5 or 7 points at a time. If South Africa wins the next Rugby World Cup and scores 34 points in the final, the highest number of times 3 points could have been scored by South Africa is (A) 6 (B) 7 (C) 8 (D) 9 (E) 10
Solution
We need to be a multiple of , so , like , must have remainder after division by . For the largest possible multiple of we need the smallest such value of , which is . Then .
Final answer
D
Techniques
Techniques: modulo, size analysis, order analysis, inequalitiesModular Arithmetic