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

Revision as of 00:02, 3 February 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

Video Solution by Cool Math Problems

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

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

@@ Line 27: / Line 27: @@
 -vockey
+== Video Solution by Cool Math Problems ==
+https://youtu.be/BRnILzqVwHk?si=kOvMjPSxqVZR8Mmt&t=89
 ==Vide Solution 1 by SpreadTheMathLove==
@@ Line 34: / Line 37: @@
 https://youtu.be/VP7g-s8akMY?si=P0Nar6jhTGl1yKZb&t=427
 ~hsnacademy
-== Video Solution by Cool Math Problems ==
-https://youtu.be/BRnILzqVwHk?si=kOvMjPSxqVZR8Mmt&t=89
 ==Video Solution by Thinking Feet==

2025 AMC 8 (Problems • Answer Key • Resources)
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