Average of five two-digit consecutive even natural numbers is (x + 10), and the average of five two-digit consecutive odd natural numbers is (y - 5). When each set is arranged in increasing order, the sum of the second even number and the fourth odd number is 71. The fifth odd number is nine less than the second even number. Which of the following statement(s) is/are true?
I. The difference between the second even number and the fourth odd number is 1.
II. The fourth even number is not a perfect square.
III. The first odd number is 31.

Five even numbers: (x + 6), (x + 8), (x + 10), (x + 12), (x + 14) Five odd numbers: (y - 9), (y - 7), (y - 5), (y - 3), (y - 1) Given, (x + 8) + (y - 3) = 71 Or, x + y = 66 ------ (I) (y - 1) = (x + 8) - 9 Or, x - y = -2 --------- (II) On adding equation I and II, We get, x + y + x - y = 66 - 2 Or, 2x = 64 Or, x = 32 On putting value of x in equation I, We get, y = 66 - 32 = 34 So, the five even numbers: 38, 40, 42, 44, 46 And the five odd numbers: 25, 27, 29, 31, 33 Statement I: Required difference = 40 - 31 = 9 (Statement is False) Statement II: 44 is not a perfect square. (Statement is True) Statement III: First odd number is 25. (Statement is False) Hence, option D.