Problem 11 · 2012 Math Kangaroo
Medium
Counting & Probability
sum-constraint
Grandmother baked 20 ginger biscuits for her grandchildren. She decorated them with raisins and nuts. First she decorated 15 with raisins, and then 15 with nuts. No biscuit was left plain. How many biscuits were decorated with both raisins and nuts?
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Answer: E — 10
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Hint 1 of 2
Adding the raisin biscuits and the nut biscuits double-counts the ones with both.
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Hint 2 of 2
The overlap is (15 + 15) - 20.
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Approach: overlap of two groups
- 15 biscuits got raisins and 15 got nuts, a total of 15 + 15 = 30 'decorations'.
- But there are only 20 biscuits and none was left plain, so the extra 30 - 20 = 10 decorations come from biscuits counted twice.
- Those 10 biscuits have both raisins and nuts.
- The answer is 10.
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