Homeschool Maths Puzzles with Answers: The “Average” Question

The average of 5 numbers is 73. When 2 numbers were removed, the average decreased by 3. What is the average of the 2 numbers that were removed?


This is part of a series on Homeschool Math Challenging Puzzles, suitable for Grades 2-4. (Of course, students of other grades are also welcome to try them out.) The questions are suitable for:

  • Homeschooling for gifted kids
  • Preparation for GEP (Gifted Education Programme) screening and selection tests
  • Preparation for Math Olympiad
  • Puzzles for kids interested in math but find school work too easy.

Answer:

This is literally an “average” question. 😛 The word “average” appears 3 times.

The trick is to focus on the total instead.

The total of the 5 numbers is: 73×5=365.

After removing 2 numbers, the average is 73-3=70.

Hence, the total of the 3 remaining numbers is: 70×3=210.

We can then conclude that, the total of the 2 removed numbers is:

365-210=155.

Hence, the average of the 2 removed numbers is: 155/2=77.5 or 75 1/2.