Problem 7 · 2014 Math Kangaroo
Easy
Logic & Word Problems
casework
Which statement is definitely correct if the following statement is false: “Everybody has solved more than 20 problems.”
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Answer: B — Somebody has solved fewer than 21 problems.
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Hint 1 of 2
The negation of 'everybody did X' is 'at least one person did not do X'.
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Hint 2 of 2
Turn 'not more than 20' into 'less than 21'.
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Approach: negate the universal statement
- 'Everybody solved more than 20' being false means at least one person did NOT solve more than 20.
- That person solved 20 or fewer, i.e. less than 21 problems.
- So somebody has solved less than 21 problems must be true.
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