答案：A

解析：

The correct answer is (A). If the tens digit is 1, there are 7 positive two-digit integers with the ones digit greater than twice the tens digit: 13,14,15,16,17,18 and 19. If the tens digit is 2, there are 5 positive two-digit integers with the ones digit greater than twice the tens digit: 25, 26, 27, 28 and 29. If the tens digit is 3, there are 3 positive two-digit integers with the ones digit greater than twice the tens digit: 37, 38 and 39. If the tens digit is 4, there is 1 positive two-digit integer with the ones digit greater than twice the tens digit: . If the tens digit is equal to or greater than 5, then the ones digits, which cannot be greater than 9, is not greater than twice the tens digit. Therefore, there is a total of 7 + 5 + 3 + 1 = 16 positive two-digit integers for which the ones digit is greater than twice the tens digit.