Difference between revisions of "2002 AMC 10B Problems/Problem 25"
(→Solution) |
m (→Problem) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list? | + | When <math>15</math> is appended to a list of integers, the mean is increased by <math>2</math>. When <math>1</math> is appended to the enlarged list, the mean of the enlarged list is decreased by <math>1</math>. How many integers were in the original list? |
<math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math> | <math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math> | ||
Revision as of 14:48, 4 June 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 
.
