Multiple choice

There are five positive observations. Average of the first three observations is 8 and that of the last three observations is 6. If the average of all five observations is 6, what is the third observation?

  1. 10

  2. 9

  3. 12

  4. 14

  5. 6
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C Correct answer
Explanation

Let observations be a, b, c, d, e. (a+b+c)/3 = 8 => a+b+c = 24. (c+d+e)/3 = 6 => c+d+e = 18. (a+b+c+d+e)/5 = 6 => a+b+c+d+e = 30. (a+b+c) + (c+d+e) - (a+b+c+d+e) = c. So 24 + 18 - 30 = 12.

AI explanation

The sum of the first three observations is 3 multiplied by 8, equaling 24, and the sum of the last three observations is 3 multiplied by 6, equaling 18. Because the average of all five observations is 6, their total sum is 5 multiplied by 6, or 30. When you add the sum of the first three and the sum of the last three, the third observation is counted twice, so subtracting the total sum of all five observations from this combined sum gives 24 plus 18 minus 30, resulting in a value of 12 for the third observation.

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