Difference between revisions of "2015 AMC 8 Problems/Problem 5"

Latest revision as of 19:52, 12 May 2023

Problem

Billy's basketball team scored the following points over the course of the first $11$ games of the season. If his team scores $40$ in the $12^{th}$ game, which of the following statistics will show an increase?

$42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73$

$\textbf{(A) } \text{range} \qquad \textbf{(B) } \text{median} \qquad \textbf{(C) } \text{mean} \qquad \textbf{(D) } \text{mode} \qquad \textbf{(E) } \text{mid-range}$

Solutions

Solution 1

When they score a $40$ on the next game, the range increases from $73-42=31$ to $73-40=33$ . This means the $\boxed{\textbf{(A) } \text{range}}$ increased.

Note: The range is defined to be the difference of the largest element and the smallest element of a set.

Solution 2

Because $40$ is less than the score of every game they've played so far, the measures of center will never rise. Only measures of spread, such as the $\boxed{\textbf{(A)}~\text{range}}$ , may increase.

Video Solution (HOW TO THINK CRITICALLY!!!)

https://youtu.be/3_D17-g3K-M

~Education, the Study of Everything

Video Solution

https://www.youtube.com/watch?v=QyBp_12cdGo&list=PL9t_YdPye18V_epxUUbwHTQNeHYBo7a1-&index=9&ab_channel=WhyMath

~savannahsolver

2015 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 1: / Line 1: @@
-Billy's basketball team scored the following points over the course of the first 11 games of the season:
+==Problem==
+Billy's basketball team scored the following points over the course of the first <math>11</math> games of the season. If his team scores <math>40</math> in the <math>12^{th}</math> game, which of the following statistics will show an increase?
 <cmath>42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73</cmath>
-If his team scores 40 in the 12th game, which of the following statistics will show an increase?
-<math>
+<math>\textbf{(A) } \text{range} \qquad \textbf{(B) } \text{median} \qquad \textbf{(C) } \text{mean} \qquad \textbf{(D) } \text{mode} \qquad \textbf{(E) } \text{mid-range} </math>
-\textbf{(A) } \text{range} \qquad
-\textbf{(B) } \text{median} \qquad
+==Solutions==
-\textbf{(C) } \text{mean} \qquad
+===Solution 1===
-\textbf{(D) } \text{mode} \qquad
-\textbf{(E) } \text{mid-range}
+When they score a <math>40</math> on the next game, the range increases from <math>73-42=31</math> to <math>73-40=33</math>.  This means the <math>\boxed{\textbf{(A) } \text{range}}</math> increased.
-</math>
+Note: The range is defined to be the difference of the largest element and the smallest element of a set.
+===Solution 2===
+Because <math>40</math> is less than the score of every game they've played so far, the measures of center will never rise. Only measures of spread, such as the <math>\boxed{\textbf{(A)}~\text{range}}</math>, may increase.
+==Video Solution (HOW TO THINK CRITICALLY!!!)==
+https://youtu.be/3_D17-g3K-M
+~Education, the Study of Everything
+==Video Solution==
+https://www.youtube.com/watch?v=QyBp_12cdGo&list=PL9t_YdPye18V_epxUUbwHTQNeHYBo7a1-&index=9&ab_channel=WhyMath
+~savannahsolver
-When they score <math>40</math>, the range increases from <math>73-42=31</math> to <math>73-40=33</math>.  This means the <math>\boxed{\textbf{(A) } \text{range}}</math> increased.
 ==See Also==
 {{AMC8 box|year=2015|num-b=4|num-a=6}}
 {{MAA Notice}}

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