Difference between revisions of "2024 AMC 10B Problems/Problem 15"
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==Problem== | ==Problem== | ||
A list of <math>9</math> real numbers consists of <math>1</math>, <math>2.2</math>, <math>3.2</math>, <math>5.2</math>, <math>6.2</math>, <math>7</math>, as well as <math>x</math>, <math>y</math> , and <math>z</math> with <math>x</math> <math>\le</math> <math>y</math> <math>\le</math> <math>z</math>. The range of the list is <math>7</math>, and the mean and the median are both positive integers. How many ordered triples (<math>x</math>, <math>y</math>, <math>z</math>) are possible? | A list of <math>9</math> real numbers consists of <math>1</math>, <math>2.2</math>, <math>3.2</math>, <math>5.2</math>, <math>6.2</math>, <math>7</math>, as well as <math>x</math>, <math>y</math> , and <math>z</math> with <math>x</math> <math>\le</math> <math>y</math> <math>\le</math> <math>z</math>. The range of the list is <math>7</math>, and the mean and the median are both positive integers. How many ordered triples (<math>x</math>, <math>y</math>, <math>z</math>) are possible? | ||
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<math>\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } \text{infinitely many}</math> | <math>\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } \text{infinitely many}</math> | ||
Revision as of 08:05, 14 November 2024
Problem
A list of 
real numbers consists of 
, 
, 
, 
, 
, 
, as well as 
, 
, and 
with 
. The range of the list is , and the mean and the median are both positive integers. How many ordered triples (, , ) are possible?
Solution 1
See also
| 2024 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
