Problem 6 · 2020 Math Kangaroo
Medium
Counting & Probability
Arithmetic & Operations
careful-countingcasework
Bia has the five coins shown. She goes to the grocery store to buy one fruit, paying with exactly three of the coins and receiving no change. Among the fruit prices below, which one can she NOT pay for?
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Answer: C — 1.40
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Hint 1 of 2
The coins are 1.00, 0.50, 0.25, 0.10 and 0.05; she uses exactly three of them with no change.
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Hint 2 of 2
Check each price: one of the listed totals simply has no three-coin combination.
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Approach: test each price against all three-coin sums
- The five coins are R$1.00, 0.50, 0.25, 0.10 and 0.05.
- 1.30 = 1.00+0.25+0.05, 1.35 = 1.00+0.25+0.10, 1.55 = 1.00+0.50+0.05, 1.75 = 1.00+0.50+0.25 - all work.
- For 1.40 no choice of three coins adds up (1.00 leaves 0.40 from two coins, impossible; without the 1.00 two coins fall far short).
- So she cannot buy the fruit costing 1.40.
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