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2014 Math Kangaroo

Problem 7

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
  1. 'Everybody solved more than 20' being false means at least one person did NOT solve more than 20.
  2. That person solved 20 or fewer, i.e. less than 21 problems.
  3. So somebody has solved less than 21 problems must be true.
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