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Difference between revisions of "2018 AMC 8 Problems/Problem 13"

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Say Laila gets a value of <math>x</math> on her first 4 tests, and a value of <math>y</math> on her last test. Thus, <math>4x+y=410.</math>  
 
Say Laila gets a value of <math>x</math> on her first 4 tests, and a value of <math>y</math> on her last test. Thus, <math>4x+y=410.</math>  
  
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The value <math>y</math> has to be greater than 82, because otherwise she would receive the same score on her last test. Additionally, the greatest value for y is 98 (as y=100 would give x as a decimal), so therefore the greatest value <math>x</math> can be is 98. As a result, only <math>4</math> numbers work, <math>86, 90, 94</math> and <math>98</math>. Thus the answer is <math>\boxed{\textbf{(A) }4}</math>.
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The value <math>y</math> has to be greater than <math>82</math>, because otherwise she would receive the same score on her last test. Additionally, the greatest value for <math>y</math> is <math>98</math> (as <math>y=100</math> would make <math>x</math> as a decimal), so therefore the greatest value <math>x</math> can be is <math>98</math>. As a result, only <math>4</math> numbers work, <math>86, 90, 94</math> and <math>98</math>. Thus the answer is <math>\boxed{\textbf{(A) }4}</math>.
  
 
== Video Solutions ==
 
== Video Solutions ==

Revision as of 16:11, 5 January 2022

Problem

Laila took five math tests, each worth a maximum of 100 points. Laila's score on each test was an integer between 0 and 100, inclusive. Laila received the same score on the first four tests, and she received a higher score on the last test. Her average score on the five tests was 82. How many values are possible for Laila's score on the last test?

$\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }9\qquad\textbf{(D) }10\qquad \textbf{(E) }18$

Solution

Say Laila gets a value of $x$ on her first 4 tests, and a value of $y$ on her last test. Thus, $4x+y=410.$

The value $y$ has to be greater than $82$, because otherwise she would receive the same score on her last test. Additionally, the greatest value for $y$ is $98$ (as $y=100$ would make $x$ as a decimal), so therefore the greatest value $x$ can be is $98$. As a result, only $4$ numbers work, $86, 90, 94$ and $98$. Thus the answer is $\boxed{\textbf{(A) }4}$.

Video Solutions

https://youtu.be/viShU5koGtk

https://youtu.be/HISL2-N5NVg?t=3251

~ pi_is_3.14

See Also

2018 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 12 		Followed by
Problem 14
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

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