Multiple choice

In a school, there are two sections, X and Y, each with a certain number of students. In Section X, there are 30 students with an average score of 75, while in Section Y, there are 40 students with an average score of 80. The highest and lowest scores in Section X are 90 and 60, respectively, and in Section Y, they are 95 and 70, respectively. If 10 students from Section Y transfer to Section X, what could be the new minimum and maximum average scores for Section X, respectively?

  1. 63.75 and 75

  2. 67.75 and 75

  3. 73.75 and 80

  4. 83.75 and 90

  5. 87.75 and 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Section X: 30 students, avg 75, total 2250. Section Y: 40 students, avg 80, total 3200. Transfer 10 students from Y to X. New X total = 2250 + sum(10 students from Y). New X count = 40. Min sum of 10 students from Y = 10 * 70 = 700. Max sum = 10 * 95 = 950. Min avg = (2250+700)/40 = 2950/40 = 73.75. Max avg = (2250+950)/40 = 3200/40 = 80.

AI explanation

Section X currently has 30 students with a total score of 30 times 75, giving 2250, and the 10 transferring students from Section Y have a total score between 10 times 70 and 10 times 95, giving 700 to 950. The new maximum average for Section X is found by adding the maximum possible transfer score to Section X's total and dividing by the new count of 40 students, so (2250 + 950) divided by 40 equals 80. The new minimum average is calculated by adding the minimum transfer score to Section X's total and dividing by 40, so (2250 + 700) divided by 40 equals 73.75. The new minimum and maximum averages are 73.75 and 80 respectively.

Keep practicing — related questions