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How many pairs are possible of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 30.

How many pairs are possible of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 30. Correct Answer 2

CONCEPT :

Let x be the smaller of the two consecutive odd natural number so that the other odd number will be x +2.

CALCULATION:

Let x be the smaller of the two consecutive odd natural numbers, so that the other one is x +2. 

we have x > 10 . . . . . . . . . . . . .  (1) 

and x + ( x + 2) < 30  . . . . . . . . .  (2) 

On solving (2), we get 2x + 2 < 30

Therefore  x < 14 . . . . . . . . . . . (3)

From (1) and (3), we get 10 < x < 14

Since x is an odd number, x can take the values 11, 13, 15, and 17. So, the required possible pairs will be (11, 13), (13, 15).

So only two pairs of odd numbers are possible.

Therefore option (2) is the correct answer.

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