Difference between revisions of "1996 AJHSME Problems/Problem 12"
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Latest revision as of 23:24, 4 July 2013
Contents
Problem 12
What number should be removed from the list
![\[1,2,3,4,5,6,7,8,9,10,11\]](http://latex.artofproblemsolving.com/3/9/9/3997f2316718e3ba0050cf5098486f6f7799080d.png)
so that the average of the remaining numbers is 
?
Solution 1
Adding all of the numbers gives us 
as the current total. Since there are 
numbers, the current average is 
. We need to take away a number from the total and then divide the result by 
because there will only be numbers left to give an average of . Setting up the equation:
Thus, the answer is 
Solution 2
Similar to the first solution, the current total is 
. Since there are numbers on the list, taking 
number away will leave numbers. If those numbers have an average of , then those numbers must have a sum of 
. Thus, the number that was removed must be 
, and the answer is .
See Also
| 1996 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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. 
