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The average of 8 numbers is 15. If one number is excluded, the average of the re

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Question: The average of 8 numbers is 15. If one number is excluded, the average of the remaining numbers becomes 12. What is the excluded number?

Options:

  1. 24
  2. 20
  3. 18
  4. 16

Correct Answer: 20

Solution: 

The total sum of the 8 numbers is 8 * 15 = 120. Let the excluded number be x. The sum of the remaining 7 numbers is 120 - x, and their average is (120 - x)/7 = 12. Thus, 120 - x = 84, leading to x = 36.

The average of 8 numbers is 15. If one number is excluded, the average of the re

Practice Questions

Q1
The average of 8 numbers is 15. If one number is excluded, the average of the remaining numbers becomes 12. What is the excluded number?
  1. 24
  2. 20
  3. 18
  4. 16

Questions & Step-by-Step Solutions

The average of 8 numbers is 15. If one number is excluded, the average of the remaining numbers becomes 12. What is the excluded number?
  • Step 1: Calculate the total sum of the 8 numbers. Since the average is 15, multiply 15 by 8. This gives you 120.
  • Step 2: Let the excluded number be represented as 'x'.
  • Step 3: The sum of the remaining 7 numbers after excluding 'x' is 120 - x.
  • Step 4: The average of the remaining 7 numbers is given as 12. To find the sum of these 7 numbers, multiply 12 by 7. This gives you 84.
  • Step 5: Set up the equation: 120 - x = 84.
  • Step 6: Solve for 'x' by subtracting 84 from 120. This gives you x = 36.
  • Average Calculation – Understanding how to calculate the average and manipulate sums based on averages.
  • Algebraic Manipulation – Using algebra to solve for an unknown variable in a given equation.
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