Problem 10 · 2022 Math Kangaroo
Medium
Logic & Word Problems
work-backward
There are 5 people to choose from on a ballot paper. After counting 90 % of the votes the intermediate result looks as shown in the table. How many of the 5 people cannot win the election anymore?
| Alex | Bella | Clint | Diana | Eddy |
|---|---|---|---|---|
| 14 | 11 | 10 | 8 | 2 |
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Answer: B — 2
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Hint 1 of 2
The 45 counted votes are 90%, so first find the total number of votes.
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Hint 2 of 2
A candidate is out if even all remaining votes cannot catch the current leader.
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Approach: find remaining votes, test who can still overtake the leader
- Counted votes 14+11+10+8+2 = 45 are 90%, so total = 50 and 5 votes remain.
- Leader Alex has 14. A rival can win only if their votes + 5 > 14, i.e. they have at least 10 now.
- Diana (8) and Eddy (2) reach at most 13 and 7, so they cannot win; the others still can.
- So 2 people can no longer win.
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