**Solution:**

Let the two consecutive odd positive integers be x and x + 2.

x < 10, x + 2 < 10, x + (x + 2) > 11

x + 2 < 10

x < 8

x + (x + 2) > 11

2x + 2 > 11

2x > 9

x > 9/2

i.e 8 > x > 9/2

Thus, the required pairs of consecutive odd positive integers are (5, 7) and (7, 5).