Art of Problem Solving
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2024 AMC 10B Problems/Problem 15: Difference between revisions

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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>


==Solution 1==
==Video Solution 1 by Pi Academy (Fast and Easy ⚡🚀)==
 
https://youtu.be/YqKmvSR1Ckk?feature=shared
 
~ Pi Academy


==See also==
==See also==
{{AMC10 box|year=2024|ab=B|num-b=14|num-a=16}}
{{AMC10 box|year=2024|ab=B|num-b=14|num-a=16}}
{{MAA Notice}}
{{MAA Notice}}

Revision as of 10:03, 14 November 2024

Problem

A list of $9$ real numbers consists of $1$, $2.2$, $3.2$, $5.2$, $6.2$, $7$, as well as $x$, $y$ , and $z$ with $x$ $\le$ $y$ $\le$ $z$. The range of the list is $7$, and the mean and the median are both positive integers. How many ordered triples ($x$, $y$, $z$) are possible?

$\textbf{(A) } 1 \qquad \textbf{(B) } 2 \qquad \textbf{(C) } 3 \qquad \textbf{(D) } 4 \qquad \textbf{(E) } \text{infinitely many}$

Video Solution 1 by Pi Academy (Fast and Easy ⚡🚀)

https://youtu.be/YqKmvSR1Ckk?feature=shared

~ Pi Academy

See also

2024 AMC 10B (ProblemsAnswer KeyResources)
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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: Unable to save thumbnail to destination