Multiple choice

The average (arithmetic mean) of a particular set of seven numbers is $12$. When one of the numbers is replaced by the number $6$, the average of the set increases to $15$. What is the number that was replaced?

  1. $-10$
  2. $-15$
  3. $-12$
  4. $0$
  5. $12$
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B Correct answer
Explanation

Initial sum = 7 * 12 = 84. Let the replaced number be x. New sum = 84 - x + 6. New average = 15, so 84 - x + 6 = 7 * 15 = 105. 90 - x = 105, so x = -15.

AI explanation

The initial sum of the seven numbers is 7 times 12 = 84. After replacement, the new sum is 7 times 15 = 105. If the replaced number is x, the equation is 84 minus x + 6 = 105, which means 90 minus x = 105, giving x = negative 15. The question contains conflicting logic since replacing a negative number with a positive number increased the sum, meaning the replaced number was negative 15.

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