Difference between revisions of "2002 AMC 10B Problems/Problem 25"
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Revision as of 19:29, 28 December 2011
Problem
When is appended to a list of integers, the mean is increased by
. When
is appended to the enlarged list, the mean of the enlarged list is decreased by
. How many integers were in the original list?
Solution
Let be the sum of the integers and
be the number of elements in the list. Then we get the equations
and
. With a little work, the solution is found to be
.
See also
2002 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last problem | |
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 |