2011 AMC 8 Problem 21
Attempt Problem 21 of the 2011 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 2011 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Students guess that Norb’s age is and Norb says, “At least half of you guessed too low, two of you are off by one, and my age is a prime number.” How old is Norb?
Answer: C
Small hint:
The two guesses off by one force Norb near either or .
Big hint:
At least half too low puts Norb above the fifth listed guess.
Solution:
The first part of the statement means that Norb’s age is greater than
The second part means that Norb’s age is either between and or between and
Since is prime and is not, Norb’s age is
Thus, C is the correct answer.
Problem 21 in other years
- 1985 AMC 8
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