Question

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

Answer 1

Given:

• Positive integers, both if which are larger than 5 such that sum is less than 23.

To Find:

• Find all the pairs of consecutive even positive integers.

Solution:

Let the smaller of the two consecutive even positive integers be x.

∴ Other integer = x + 2

According to Question, both the integers are larger than 5

∴ x > 5 ____(i)

According to Question, the sum of two integers is less than 23.

∴ x + (x + 2) < 23

$\implies$ 2x + 2 < 23

$\implies$ x < 21/2

$\implies$ x < 10.5 ____(ii)

Thus, From (i) and (ii);

We have x is an even number and it can take values 6, 8 and 10

Hence,

• Possible pairs are (6, 8), (8, 10) and (10, 12).