2014 AMC 8 Problem 10

Attempt Problem 10 of the 2014 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

The first AMC 88 was given in 19851985 and it has been given annually since that time. Samantha turned 1212 years old the year that she took the seventh AMC 8.8. In what year was Samantha born?
1979 1979
1980 1980
1981 1981
1982 1982
1983 1983
Answer: A
Concepts:agesdate and time
Small hint:
The seventh AMC 88 was six years after the first AMC 8.8.
Big hint:
Subtract Samantha’s age from that year.
Solution:
The seventh AMC 88 would have been administered 66 years after the first one. Therefore, Samantha took it in 1985+6=1991.1985 + 6 = 1991.
This means that Samantha was born 1212 years prior in 1991−12=1979.1991 - 12 = 1979.
Thus, A is the correct answer.
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