Question

Determine all pairs of consecutive even positive integers, both of which are greater than 5 such that theirsum is less than 23.

Answer 1

ANSWER

10 and 12

STEP BY STEP

Let x be the smaller of the two consecutive even positive integers, then the other even integer is x + 2.

Given x > 8 and x + (x + 2) < 25.

⇒ x > 8, and 2x + 2 < 25.

⇒ x > 8, 2x < 23

⇒ x > 8, x < 23/2

⇒ 8 < x < 23/2

⇒ x = 10,

∴ the required parity even integers is (10, 12)