Multiple choice

The average of 8 numbers is 40. If the average of the first six numbers is 30 and that of the last three numbers is 60, the sixth number is

  1. 35

  2. 30

  3. 25

  4. 40

  5. 48
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D Correct answer
Explanation

Sum of 8 numbers = 8 * 40 = 320. Sum of first 6 = 6 * 30 = 180. Sum of last 3 = 3 * 60 = 180. The 6th number is counted in both the first 6 and the last 3. Sum of 8 = (Sum of first 5) + (6th) + (Sum of last 2) = 320. (Sum of first 6) + (Sum of last 3) = 180 + 180 = 360. The overlap is the 6th number: 360 - 320 = 40.

AI explanation

The total of all eight numbers is 8 times 40, giving 320. The sum of the first six numbers is 6 times 30, which is 180, and the sum of the last three numbers is 3 times 60, which is 180. By the principle of overlapping sets, adding the sum of the first six and the last three gives 360, which counts the sixth number twice. Subtracting the overall total of 320 from 360 leaves 40, so the sixth number is 40.

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