Problem 10 · 2014 AMC 8
Easy
Arithmetic & Operations
year-arithmetic
The first AMC 8 was given in 1985 and it has been given annually since that time. Samantha turned 12 years old the year that she took the seventh AMC 8. In what year was Samantha born?
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Answer: A — 1979.
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Hint 1 of 2
Watch the off-by-one: the 1st contest was 1985, so the 7th is only 6 years later (not 7). Add the gap, not the count.
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Hint 2 of 2
Once you have the year she took it, subtract her age to land on her birth year.
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Approach: fencepost-careful year arithmetic
- The 7th AMC 8 is 6 gaps after the 1st: 1985 + 6 = 1991. (1st→7th is 6 steps, not 7 — the classic fencepost.)
- She turned 12 that year, so she was born 1991 − 12 = 1979.
- Reusable caution: the n-th item in a yearly sequence starting at year Y falls in Y + (n − 1). Counting endpoints instead of gaps is the most common slip in these problems.
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