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Question:

Find all pairs of concecutive odd natural numbers, both of which are greater than 10, such that their sum is

less than 40

Answer:

Let x be the odd natural number.

Then the other consecutive odd natural numbers is x + 2

Given that both are greater than 10

=> x > 10 and x + 2 > 10

=> x > 10 and x > 10 - 2

=> x > 10 and x > 8

=> x > 10  ..........1

Again given that their sum is less than 40

=> x + x + 2 < 40

=> 2x + 2 < 40

=> 2x < 40 - 2

=> 2x < 38

=> x < 38/2

=> x < 19 ...........2

From equation 1 and 2, we get

x > 10 and x < 19

Since x is an odd number

So, x = 11, 13, 15, 17

Since, their sum is less than 40

Hence, the required pairs of odd natural numbers are (11, 13), (13, 15), (15, 17), (17, 19)

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