The average of fifteen numbers is 45. The average of the first six numbers is…

To find the average of the remaining three numbers, first calculate the total sum of all fifteen numbers. Since their average is 45, the total sum equals 15 multiplied by 45, which is 675. Next, determine the sum of the known groups: the first six numbers average 42.5, totaling 6 * 42.5 = 255, and the last six numbers average 44.5, totaling 6 * 44.5 = 267. Subtracting these two sums from the grand total (675 - 255 - 267) leaves a remaining sum of 153 for the three unknown numbers. Dividing this remainder by 3 gives an average of 51. However, the question specifies that two of these three numbers are 41 and 46. Their sum is 87, meaning the third number must be 153 - 87 = 66. The average of the three numbers (41, 46, and 66) is indeed 51. There appears to be a discrepancy in the provided options and correct answer key, as none match the calculated average of 51. Based on standard arithmetic principles, Option A (48) is incorrect as the calculated average is 51.