Problem 1 · 2010 AMC 8
Easy
Arithmetic & Operations
addition
At Euclid Middle School the mathematics teachers are Miss Germain, Mr. Newton, and Mrs. Young. There are 11 students in Mrs. Germain's class, 8 students in Mr. Newton's class, and 9 students in Mrs. Young's class taking the AMC 8 this year. How many mathematics students at Euclid Middle School are taking the contest?
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Answer: C — 28.
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Hint 1 of 2
Each class is a separate group of students, and no student is in two of these classes — so the total is just the three counts joined together.
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Hint 2 of 2
When groups don't overlap, the whole equals the sum of the parts. Add them.
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Approach: add disjoint groups
- The three classes don't share students, so the total is just 11 + 8 + 9 = 28.
- Why this transfers: ‘how many altogether’ is a plain sum only when the groups can't overlap. The moment groups could share members (students in two clubs, say), you'd need to subtract the overlap — that's the inclusion-exclusion idea you'll meet later.
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