2025 AMC 8

Complete problem set with solutions and individual problem pages

Problem 7 Easy

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\%?

  • A.

    8

  • B.

    14

  • C.

    22

  • D.

    37

  • E.

    45

Answer:D

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}}.

 

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}}.

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