Difference between revisions of "2011 AMC 8 Problems/Problem 21"
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==Solution== | ==Solution== | ||
| − | If at least half the guesses are too low, then | + | If at least half the guesses are too low, then Norb's age must be greater than <math>36.</math> |
| − | If two of the guesses are off by one, then his age is in between two guesses whose difference is <math>2.</math> It could <math>31,37,</math> or <math>48,</math> but because | + | If two of the guesses are off by one, then his age is in between two guesses whose difference is <math>2.</math> It could be <math>31,37,</math> or <math>48,</math> but because his age is greater than <math>36</math> it can only be <math>37</math> or <math>48.</math> |
| − | Lastly, | + | Lastly, Norb's age is a prime number so the answer must be <math>\boxed{\textbf{(C)}\ 37}</math> |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2011|num-b=20|num-a=22}} | {{AMC8 box|year=2011|num-b=20|num-a=22}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 23:08, 9 November 2018
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 
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 | ||
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