Multiple choice

A dataset originally consists of 10 values with an average value of 50 each. After adding 3 new consecutive integral values, the average of the entire dataset increases to 53. What is the maximum value among these 3 consecutive integral values?

  1. 62

  2. 63

  3. 64

  4. 65

  5. 66
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C Correct answer
Explanation

Initial sum = 10 * 50 = 500. New sum = 13 * 53 = 689. The sum of the 3 new integers is 689 - 500 = 189. Let the integers be x-1, x, x+1. Their sum is 3x = 189, so x = 63. The values are 62, 63, 64. The maximum is 64.

AI explanation

The initial sum of the 10 values is 10 times 50, which is 500. The new sum for 13 values must be 13 times 53, which is 689, meaning the three new values sum to 189. Since the values are consecutive integers, their average is 189 divided by 3, which is 63; therefore, the sequence is 62, 63, 64, making the maximum value 64.

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