2025 AMC 8 Problems/Problem 7: Difference between revisions

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Latest revision as of 14:47, 10 November 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

@@ Line 1: / Line 1: @@
-==Problem 7==
+== 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 ==
+<imath>50</imath> people scored at least <imath>80\%</imath>, and out of these <imath>50</imath> people, <imath>13</imath> of them earned a score that was not less than <imath>90\%</imath>, so the number of people that scored in between at least <imath>80\%</imath> and less than <imath>90\%</imath> is <imath>50-13 = \boxed{\text{(D)\ 37}}</imath>.
+~Soupboy0
-<math>5</math> students earned a score of at least <math>95</math>%,
+== Solution 2 ==
-<math>13</math> students earned a score of at least <math>90</math>%,
+Let <imath>a</imath> denote the number of people who had a score of at least <imath>85</imath>, but less than <imath>90</imath>, and let <imath>b</imath> denote the number of people who had a score of at least <imath>80</imath> but less than <imath>85</imath>. Our answer is equal to <imath>a+b</imath>. We find <imath>a = 27 - 13 = 14</imath>, while <imath>b = 50 - 27 = 23</imath>. Thus, the answer is <imath>23 + 14 = \boxed{\text{(D)\ 37}}</imath>.
-<math>27</math> students earned a score of at least <math>85</math>%,
+-vockey
-<math>50</math> students earned a score of at least <math>80</math>%,
+== 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
-How many students earned a score of at least 80% and less than 90%?
+== Video Solution 3 ==
+[//youtu.be/VP7g-s8akMY?si=P0Nar6jhTGl1yKZb&t=427 ~hsnacademy]
-<math>\textbf{(A)}\ 8\qquad \textbf{(B)}\ 14\qquad \textbf{(C)}\ 22\qquad \textbf{(D)}\ 37\qquad \textbf{(E)}\ 45 </math>
+== 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
-==Solution==
+== See Also ==
-<math>50</math> people scored at least <math>80\%</math>, and out of these <math>50</math> people, <math>13</math> of them earned at least <math>90\%</math>, so the people that scored in between <math>80\%</math> and <math>90\%</math> is <math>50-13 = \boxed{\text{(D)\ 37}}</math>.
+{{AMC8 box|year=2025|num-b=6|num-a=8}}
+{{MAA Notice}}
+[[Category:Introductory Number Theory Problems]]

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