2025 AMC 8 Problems/Problem 7

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

See Also

2025 AMC 8 (ProblemsAnswer KeyResources)
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

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