Problem 1 · 2000 AMC 8
Easy
Arithmetic & Operations
ages
Aunt Anna is 42 years old. Caitlin is 5 years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?
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Answer: B — 16.
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Hint 1 of 2
The question asks about Caitlin, but you can't reach her directly — she's defined through Brianna, who's defined through Aunt Anna. Find the one age you CAN pin down first.
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Hint 2 of 2
When ages are chained ('A is half of B, C is 5 less than A'), resolve them in the order the clues give you, never the order the question asks for.
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Approach: resolve the age chain from the known link outward
- Only one age is fully known: Aunt Anna's 42. Brianna is the link tied to her — 'half as old' means 42 ÷ 2 = 21.
- Now Caitlin is reachable: 5 younger than Brianna, so 21 − 5 = 16.
- You'll see it again: word problems often define the thing you want through other things — start at the fully-known value and walk the chain toward the target.
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