2022 AMC 10B Problems/Problem 10
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Problem
Camila writes down five positive integers. The unique mode of these integers is 
greater than their median, and the median is greater than their arithmetic mean. What is the least possible value for the mode?
Solution
Let 
be the median. It follows that the two largest integers are 
Let 
and 
be the two smallest integers such that 
The sorted list is ![\[a,b,M,M+2,M+2.\]](http://latex.artofproblemsolving.com/9/a/0/9a0ec4d708d73a1c4bb1a86ddef45f82d1310e0c.png)
~MRENTHUSIASM
See Also
| 2022 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 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 AMC 10 Problems and Solutions | ||
| 2022 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 6 |
Followed by Problem 8 |
| 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 AMC 12 Problems and Solutions | |
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