Multiple choice

In a group of 16 students, the age of the tallest student is 16 years and the age of the shortest student is 3/4 of the age of the tallest one. If the ages of the tallest and the shortest students are excluded, then the average age of 14 students becomes 1 year less than the average age of all students. What is the average age of 16 students?

  1. 6 years

  2. 14 years

  3. 7 years

  4. 21 years

  5. Cannot be Determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S be the sum of ages of 16 students, A = S/16. Tallest = 16, Shortest = 3/4 * 16 = 12. Sum of remaining 14 = S - 28. Average of 14 = (S - 28)/14 = A - 1. S - 28 = 14A - 14. Since S = 16A, 16A - 28 = 14A - 14. 2A = 14, A = 7.

AI explanation

Let the average age of all 16 students be A; the sum of their ages is 16 times A. The shortest student is 16 multiplied by 3 fourths, which equals 12 years. Excluding the tallest and shortest, the average age of the remaining 14 students is A minus 1, so their sum is 14 multiplied by (A minus 1). This yields the equation 16 times A minus 16 minus 12 equals 14 times A minus 14. Solving for A gives 2 times A equals 14. The result is 7 years.

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