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

Revision as of 23:58, 31 January 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

$50$ people scored at least $80\%$ , and out of these $50$ people, $13$ of them earned at least $90\%$ , so the people that scored in between $80\%$ and $90\%$ is $50-13 = \boxed{\text{(D)\ 37}}$ .

~Soupboy0

Solution 2

Let $b$ denote the number of people who had a score of at least $85$ , but less than $90$ . Similarly, let $d$ be the number of people who had a score of at least $80$ but less than $85$ . Now we can see the question is just asking for $c+d$ , we find $c = 27 - 13 = 14$ , while $d = 50 - 27 = 23$ . Thus, the answer is $23 + 14 = \boxed{\text{(D)\ 37}}$ .

-vockey

Vide Solution 1 by SpreadTheMathLove

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

Video Solution (A Clever Explanation You’ll Get Instantly)

https://youtu.be/VP7g-s8akMY?si=P0Nar6jhTGl1yKZb&t=427 ~hsnacademy

Video Solution by Thinking Feet

https://youtu.be/PKMpTS6b988

Video Solution by Daily Dose of Math

https://youtu.be/nkpdskFVgdM

~Thesmartgreekmathdude

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 22: / Line 22: @@
 ~Soupboy0
+==Solution 2==
+Let <math>b</math> denote the number of people who had a score of at least <math>85</math>, but less than <math>90</math>. Similarly, let <math>d</math> be the number of people who had a score of at least <math>80</math> but less than <math>85</math>. Now we can see the question is just asking for <math>c+d</math>, we find <math>c = 27 - 13 = 14</math>, while <math>d = 50 - 27 = 23</math>. Thus, the answer is <math>23 + 14 = \boxed{\text{(D)\ 37}}</math>.
+-vockey
 ==Vide Solution 1 by SpreadTheMathLove==
 https://www.youtube.com/watch?v=jTTcscvcQmI

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