**Solution:**

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

x > 5, x + 2 > 5, x + (x + 2) < 23

x > 5, x + 2 > 5 ⇒x > 5.

2x + 2 < 23

2x < 21

x < 21/2

i.e 21/2 > x > 5

Thus, the required pairs of consecutive odd positive integers are (6, 8) and (8, 10).