Problem 5 · 2013 Math Kangaroo
Easy
Number Theory
digit-sumcareful-counting
Five children are talking about the number 325. Andreas: “It is a three-digit number.” Boris: “All the digits are different.” Sara: “The digit sum is 10.” Gerda: “The units digit is 5.” Daniela: “All the digits are odd.” Who has made a mistake?
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Answer: E — Daniela
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Hint 1 of 2
Check each child's statement against the actual number 325.
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Hint 2 of 2
One statement is simply false — look at whether every digit is really odd.
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Approach: test each claim about 325
- 325 is a three-digit number (Andreas correct), its digits 3, 2, 5 are all different (Boris correct).
- 3+2+5 = 10 (Sara correct) and the units digit is 5 (Gerda correct).
- But 2 is even, so 'all the digits are odd' is wrong — that is Daniela.
Mark:
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