Question

Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

Answer 1

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).