Question

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

Answer 1

Hint: Even integers are those that are divisible by two, and consecutive numbers are those that are taken in a sequential order (1,2,3,4.....). So, try to get even-consecutive positive integers greater than 5 using the preceding definition, and then use the given condition to get the number of pairs.

Complete step by step answer:
To solve the problem, we must first comprehend the concept of consecutive even integers. As previously stated, even integers are positive integers that are divisible by two. It denotes a number that is a multiple of two. The term "consecutive numbers" refers to numbers that are written in a continuous fashion, such as (2,3) and (4,5).
As a result, the meaning of consecutive even integers is that the numbers will always be in the difference of two, because there will always be an odd number between two consecutive even integers. As an example, even integers can be written as (4,6), (6,8), (8,10) and so on.
Now let’s come to the question: we need to find the pairs of all successive even positive numbers that are both greater than 5, and whose sum is less than 23.
The numbers 6, 7, 8, 9, 10,11, 12.. can be used to represent positive integers greater than five.
As a result, even positive integers greater than five can be written as 6,8,10 and so on.
We now know that we must discover successive even integers, which indicates that the even integers used to make a pair must be in a continuous pattern. As a result, we can acquire all the even positive numbers in a row as (6,8), (8,10), (10,12), and so on.
Now, we need to find those pairs which will give the sum of numbers in pairs less than 23.
Now, we can observe the pairs of consecutive even positive integer and get that sum of
(6,8) is 14; (8,10) is 18; (10,12) is 22; and (12,14) is 26 and so on.
So, we get that there are only three pairs which will have a sum less than 23 that are (6,8),(8,10) and (10,12).
Hence (6,8),(8,10) and (10,12) are the correct answers of the above expression.

Note:
 It's easy to be confused with the term "consecutive even integer," because consecutive refers to integers that are repeated (i.e. 1,2,3,4,....). However, other phrases, such as ‘even,' imply that we must only use continuous even positive numbers (2,4,6,8).