Question

Find all pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum in more than 11.

Answer 1

Hint: Odd integers means the integers which are not divisible by 2 and consecutive numbers means the numbers taken are in continuous manner (1,2,3,4…..). So try to use the above definition to get odd-consecutive positive integers less than 10 and use the given condition to get the number of pairs.

Complete step-by-step answer:
For solving the problem, we need to understand the term consecutive odd integers. So, as we know odd integers are those positive integers which are not divisible by 2. It means the number which is not a multiple of ‘2’ is an odd number. And consecutive numbers mean the numbers taken in continuous form i.e. (2,3), (4,5) are the consecutive integers.
Hence, the meaning of consecutive odd integers means the numbers will occur in difference of 2 as there will always be an even number between two continuous odd integers. So, an example of consecutive odd integers can be given as (3,5), (5,7), (7,9), (11, 13) etc.
Now coming to the question as we need to determine the pairs of all consecutive odd positive integers both of which should be smaller than 10, such that their sum is more than 11.
Positive integers less than 10 can be given as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
So, odd positive integers less than 10 can be given as 1, 3, 5, 7, 9.
Now, we know that we need to find consecutive odd integers, it means odd integers taken for making a pair should be in continuous manner. So, we can get all the consecutive odd positive integers as (1,3), (3,5), (5,7), (7,9).
Now, we need to find those pairs which will give the sum of numbers in pairs more than 11.
Now, we can observe the pairs of consecutive odd positive integer and get that sum of
(1,3) is 4; (3,5) is 8; (5,7) is 12; and (7,9) is 16.
So, we get that there are only two pairs which will have sum more than 11 that are (5,7) and (7,9).
Hence (5,7) and (7,9) are the correct answer of the above expression.

Note: One may get confused with the word “consecutive odd integer” as consecutive means numbers in continuous manner (i.e. 1,2,3,4,…..). But look at other terms i.e. ‘odd’ means we need to take continuous odd positive integers only (1,3,5,7,9….).