2002 AMC 10A Problems/Problem 21: Difference between revisions
this solution is due to azjps |
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==Problem== | ==Problem== | ||
The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is | |||
<math>\text{(A)}\ | <math>\text{(A)}\ 11 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 15</math> | ||
==Solution== | ==Solution== | ||
Revision as of 09:18, 27 December 2008
Problem
The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. The largest integer that can be an element of this collection is
Solution
Given 
tiles, a step removes 
tiles, leaving 
tiles behind. Now, 
, so in the next step 
tiles are removed. This gives 
, another perfect square, and the process repeats.
Thus each two steps we cycle down a perfect square, and in 
steps, we are left with 
tile.
See Also
| 2002 AMC 10A (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 AMC 10 Problems and Solutions | ||
