Multiple choice

The average of 21 numbers is 12. The average of the first 11 numbers is 9 and the average of the last 11 numbers is 15. What is the value of the middle number?

  1. 10

  2. 11

  3. 12

  4. 13
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C Correct answer
Explanation

Total sum of 21 numbers is 21 * 12 = 252. Sum of first 11 is 11 * 9 = 99. Sum of last 11 is 11 * 15 = 165. The middle number is counted twice: (99 + 165) - 252 = 264 - 252 = 12.

AI explanation

The sum of all 21 numbers is 21 multiplied by 12, which equals 252. The sum of the first 11 numbers is 11 multiplied by 9, or 99, and the sum of the last 11 numbers is 11 multiplied by 15, or 165. Adding the sums of the first and last groups gives 264, which counts the middle number twice, so subtracting the overall sum of 252 from 264 leaves the middle number as 12.

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