Multiple choice

The average of 35 results is 75 and the average of the first 18 of them is 78 and the average of the last 18 is 73. Then find the 18th number.

  1. 110

  2. 93

  3. 67

  4. 57
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B Correct answer
Explanation

Sum of all 35 numbers = 35 × 75 = 2625. Sum of first 18 = 18 × 78 = 1404. Sum of last 18 = 18 × 73 = 1314. The 18th number is counted in both the first 18 and last 18. So: Sum(first 18) + Sum(last 18) = Total + 18th number. Therefore: 1404 + 1314 = 2625 + 18th number, giving 2718 = 2625 + 18th number, so 18th number = 2718 - 2625 = 93.

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