Find pairs of consecutive even positive integers which are larger than 5 and are such that their sum is less than 20.

Let the consecutive even positive integers be x and x + 2
                                                     ...(i)
Their sum is less than 20.
           x + (x + 20) < 20  2x + 2 < 20   2x < 18  x < 9                        ...(ii)
From (i) and (ii), we have 5 < x < 9,  
But, x is given,            ∴  x = 6,  8
When                          x = 6,  x + 2 = 8
When                          x = 8,  x + 2 = 10
Hence, the two pairs that satisfy the given conditions are: 6, 8 and 10.