2011 AMC 8 Problems/Problem 21
Contents
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
Solution 2 (Alternative approach)
Since two guesses are off by one, we know that both and are in the list where is the age of Norb. Now, we know that and are and , and , and and and . From these values, we know that must be , , and . Since half of the guesses are too low, and are all too low so we can eliminate all numbers in our list lesser than or equal to . Therefore, our list has only left so the answer is .
Video Solution by OmegaLearn
https://youtu.be/HISL2-N5NVg?t=3886
~ pi_is_3.14159265
Video Solution by WhyMath
~savannahsolver
See Also
2011 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.