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

Let the required consecutive even integers be x and x + 2. Then,
`xgt5 and x +(x+2)lt23`
`rArrxgt5 and 2xlt21`
`rArr 5ltx and x lt 10.5`
`rArr 5 lt x lt 10.5`
`therefore` x can take the even integral value 6, 8 and 10.
Hence, the required pairs of even integers are (6, 8), (8, 10) and (10, 12).