Difference between revisions of "2012 AMC 8 Problems/Problem 11"
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==Problem== | ==Problem== | ||
− | The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, | + | The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and <math>x</math> are all equal. What is the value of <math>x</math>? |
<math> \textbf{(A)}\hspace{.05in}5\qquad\textbf{(B)}\hspace{.05in}6\qquad\textbf{(C)}\hspace{.05in}7\qquad\textbf{(D)}\hspace{.05in}11\qquad\textbf{(E)}\hspace{.05in}12 </math> | <math> \textbf{(A)}\hspace{.05in}5\qquad\textbf{(B)}\hspace{.05in}6\qquad\textbf{(C)}\hspace{.05in}7\qquad\textbf{(D)}\hspace{.05in}11\qquad\textbf{(E)}\hspace{.05in}12 </math> |
Revision as of 18:47, 22 December 2012
Problem
The mean, median, and unique mode of the positive integers 3, 4, 5, 6, 6, 7, and are all equal. What is the value of ?
Solution
Since there must be an unique mode, we can eliminate answer choices and . Now we need to test the remaining answer choices.
Case 1:
Mode:
Median:
Mean:
Since the mean does not equal the median or mode, can also be eliminated.
Case 2:
Mode:
Median:
Mean:
We are done with this problem, because we have found when , the condition is satisfied. Therefore, the answer is .
See Also
2012 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 |