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A set of five two-digit integers is given. The average of the first and last numbers is the middle number. The second number is half of the first number. The sum of the first three numbers is 127. The middle number is (A) and the average of the five numbers is (B). The fourth number is 62. What can be the values of (A) and (B), respectively?

1. 64, 50
2. 62, 55
3. 62, 50
4. 64, 55

Correct answer: 64, 55

Solution

Let the first number be x, the second be x/2, and the middle number be m. Since the sum of the first three numbers is 127, we get x + x/2 + m = 127. Also, the average of the first and last numbers is the middle number, so (x + last)/2 = m; with the fourth number given as 62, the consistent set gives m = 64 and the overall average as 55.

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