Let:
The smaller even positive integer be x.
Since the numbers are consecutive even integers,
the next integer is x + 2.
Given that both integers are larger than 5,
x > 5
Condition: Sum is less than 23
x + (x + 2) < 23
2x + 2 < 23
2x < 21
x < 10.5
Possible values of x:
x is an even positive integer such that
6 ≤ x < 10.5
So,
x = 6, 8, 10
Corresponding pairs:
(6, 8) → sum = 14
(8, 10) → sum = 18
(10, 12) → sum = 22
Final Answer:
The required pairs of consecutive even positive integers are:
(6, 8), (8, 10), and (10, 12)