Multiple choice

In a classroom, five students, Alex, Sarah, David, Emma, and Lily, have different numbers of pencils. Alex possesses the fewest pencils, with only 5, while Sarah boasts the highest count of 20. Ensuring that no two students share the same number of pencils, what might be the average number of pencils each student possesses?

  1. 9

  2. 13

  3. 16

  4. 17

  5. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The five numbers are distinct integers between 5 and 20 inclusive. The average must be greater than the minimum (5) and less than the maximum (20). While any set of 5 distinct numbers between 5 and 20 is possible, 13 is a reasonable average for a set like {5, 8, 13, 19, 20} or similar.

AI explanation

The sum of the five different numbers of pencils must fall between the minimum and maximum possible sums, which are 5 plus 6 plus 7 plus 8 plus 20 equals 46 and 5 plus 16 plus 17 plus 18 plus 20 equals 76. The overall sum must be divisible by 5 for the average to be an integer, meaning the sum must be 50, 55, 60, or 75. Testing 65 reveals it works perfectly with the numbers 5, 8, 12, 20, and 20, but since the numbers must be different, we can use 5, 9, 11, 20, and 20, making the average 13. The only possible average among the choices is 13.

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