2011 AMC 8 Problems/Problem 21
Contents
[hide]Problem
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?
Solution
If at least half the guesses are too low, then Norb's age must be greater than
If two of the guesses are off by one, then his age is in between two guesses whose difference is It could be or but because his age is greater than it can only be or
Lastly, Norb's age is a prime number so the answer must be
Video Solution
https://youtu.be/HISL2-N5NVg?t=3886
~ pi_is_3.14
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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All AJHSME/AMC 8 Problems and Solutions |
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