Multiple choice

The average of 18 numbers is 52. The average of the first 8 numbers is 62 and the average of the next 7 numbers is 45. If the 16th number is 6 less than the 17th number and the 17th number is one more than the 18th number, then what is the average of the 16th and 18th numbers?

  1. 39

  2. 39.5

  3. 40.5

  4. 40
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C Correct answer
Explanation

Sum of 18 = 18 * 52 = 936. Sum of first 8 = 8 * 62 = 496. Sum of next 7 = 7 * 45 = 315. Sum of 16th, 17th, 18th = 936 - 496 - 315 = 125. Let 18th = x, 17th = x+1, 16th = x+1-6 = x-5. 3x - 4 = 125, 3x = 129, x = 43. 16th = 38, 18th = 43. Average = (38 + 43) / 2 = 40.5.

AI explanation

The total sum of all 18 numbers is 18 times 52, which equals 936. The sum of the first 8 numbers is 8 times 62, giving 496, and the sum of the next 7 numbers is 7 times 45, giving 315. Subtracting these two sums from 936 leaves a remaining sum of 125 for the last three numbers. Let the 18th number be x, which makes the 17th number x plus 1 and the 16th number x minus 5. Adding these gives 3x minus 4 equals 125, so x equals 43. The average of the 16th number (38) and the 18th number (43) is 38 plus 43 divided by 2. The result is 40.5.

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