Difference between revisions of "2025 AMC 8 Problems/Problem 7"

Latest revision as of 18:42, 9 March 2025

Problem

On the most recent exam on Prof. Xochi's class,

$5$ students earned a score of at least $95\%$ ,

$13$ students earned a score of at least $90\%$ ,

$27$ students earned a score of at least $85\%$ ,

$50$ students earned a score of at least $80\%$ ,

How many students earned a score of at least $80\%$ and less than $90\%$ ?

$\textbf{(A)}\ 8\qquad \textbf{(B)}\ 14\qquad \textbf{(C)}\ 22\qquad \textbf{(D)}\ 37\qquad \textbf{(E)}\ 45$

Solution 1

$50$ people scored at least $80\%$ , and out of these $50$ people, $13$ of them earned a score that was not less than $90\%$ , so the number of people that scored in between at least $80\%$ and less than $90\%$ is $50-13 = \boxed{\text{(D)\ 37}}$ .

~Soupboy0

Solution 2

Let $a$ denote the number of people who had a score of at least $85$ , but less than $90$ , and let $b$ denote the number of people who had a score of at least $80$ but less than $85$ . Our answer is equal to $a+b$ . We find $a = 27 - 13 = 14$ , while $b = 50 - 27 = 23$ . Thus, the answer is $23 + 14 = \boxed{\text{(D)\ 37}}$ .

-vockey

Video Solution 1 by Cool Math Problems

https://youtu.be/BRnILzqVwHk?si=kOvMjPSxqVZR8Mmt&t=89

Video Solution 2 by SpreadTheMathLove

https://www.youtube.com/watch?v=jTTcscvcQmI

Video Solution 3

~hsnacademy

Video Solution 4 by Thinking Feet

https://youtu.be/PKMpTS6b988

Video Solution 5 by Daily Dose of Math

~Thesmartgreekmathdude

Video Solution(Quick, fast, easy!)

https://youtu.be/fdG7EDW_7xk

~MC

2025 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

@@ Line 1: / Line 1: @@
-The 2025 AMC 8 is not held yet. Please do not post false problems.
+== Problem ==
+On the most recent exam on Prof. Xochi's class,
+<math>5</math> students earned a score of at least <math>95\%</math>,
+<math>13</math> students earned a score of at least <math>90\%</math>,
+<math>27</math> students earned a score of at least <math>85\%</math>,
+<math>50</math> students earned a score of at least <math>80\%</math>,
+How many students earned a score of at least <math>80\%</math> and less than <math>90\%</math>?
+<math>\textbf{(A)}\ 8\qquad \textbf{(B)}\ 14\qquad \textbf{(C)}\ 22\qquad \textbf{(D)}\ 37\qquad \textbf{(E)}\ 45 </math>
+== Solution 1 ==
+<math>50</math> people scored at least <math>80\%</math>, and out of these <math>50</math> people, <math>13</math> of them earned a score that was not less than <math>90\%</math>, so the number of people that scored in between at least <math>80\%</math> and less than <math>90\%</math> is <math>50-13 = \boxed{\text{(D)\ 37}}</math>.
+~Soupboy0
+== Solution 2 ==
+Let <math>a</math> denote the number of people who had a score of at least <math>85</math>, but less than <math>90</math>, and let <math>b</math> denote the number of people who had a score of at least <math>80</math> but less than <math>85</math>. Our answer is equal to <math>a+b</math>. We find <math>a = 27 - 13 = 14</math>, while <math>b = 50 - 27 = 23</math>. Thus, the answer is <math>23 + 14 = \boxed{\text{(D)\ 37}}</math>.
+-vockey
+== Video Solution 1 by Cool Math Problems ==
+https://youtu.be/BRnILzqVwHk?si=kOvMjPSxqVZR8Mmt&t=89
+==Video Solution 2 by SpreadTheMathLove==
+https://www.youtube.com/watch?v=jTTcscvcQmI
+== Video Solution 3 ==
+[//youtu.be/VP7g-s8akMY?si=P0Nar6jhTGl1yKZb&t=427 ~hsnacademy]
+== Video Solution 4 by Thinking Feet ==
+https://youtu.be/PKMpTS6b988
+== Video Solution 5 by Daily Dose of Math ==
+[//youtu.be/nkpdskFVgdM ~Thesmartgreekmathdude]
+==Video Solution(Quick, fast, easy!)==
+https://youtu.be/fdG7EDW_7xk
+~MC
+== See Also ==
+{{AMC8 box|year=2025|num-b=6|num-a=8}}
+{{MAA Notice}}
+[[Category:Introductory Number Theory Problems]]

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