Problem 21 · 2018 Math Kangaroo
Stretch
Logic & Word Problems
work-backwardsum-constraint
At an election for student representatives there are three candidates. 130 students have voted, and the candidate with the most votes wins. Currently Samuel has 24 votes, Kevin 29 and Alfred 37. How many of the votes not yet counted does Alfred need to get in order to definitely win the election?
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Answer: E — 17
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Hint 1 of 2
Count how many votes are still uncounted, then imagine them all going to Alfred's nearest rival.
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Hint 2 of 2
Alfred must stay ahead even in that worst case.
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Approach: worst-case: rival gets all the rest
- Counted so far: 24 + 29 + 37 = 90, so 130 − 90 = 40 votes remain.
- If Alfred gets x of them, Kevin could get the other 40 − x, reaching 29 + 40 − x = 69 − x.
- Alfred wins for sure when 37 + x > 69 − x, i.e. x > 16, so he needs 17 of the remaining votes.
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