Multiple choice

The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, then the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years and is 8 years older than the youngest. What is the number of students in the class?

  1. 2

  2. 4

  3. 6

  4. 8

  5. 10
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B Correct answer
Explanation

Let n be the number of students and S be the sum of their ages. S/n = 25, so S = 25n. The oldest is 28, and the youngest is 28 - 8 = 20. Excluding them, the sum is 25n - 48, and the number of students is n - 2. The new average is (25n - 48)/(n - 2) = ((28 + 20)/2) + 2 = 26. Solving 25n - 48 = 26n - 52 gives n = 4.

AI explanation

The youngest student is 28 minus 8, which is 20 years old. The average age of the youngest and oldest is 20 plus 28, giving 48, and dividing by 2 results in 24. The average age of the remaining students is 24 plus 2, giving 26. The total age of the remaining students is 26 multiplied by n minus 2, and the total age of all students is 25 multiplied by n. The sum of the ages of the excluded students is 20 plus 28, giving 48. Therefore, 25 times n minus 26 times n minus 2 equals 48, which gives n minus 52 equals 48, so n equals 4.

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