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Question -

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



Answer -

Let us assume x be the smaller of the two consecutive odd positive integers
∴ Other integer is = x + 2
It is also given in the question that, both the integers are smaller than 10
∴ x + 2 < 10
x < 8 … (i)
Also, it is given in the question that sum off two integers is more than 11
∴ x + (x + 2) > 11
2x + 2 > 11
x > 9/2
x > 4.5 … (ii)
Thus, from (i) and (ii) we have x is an odd integer and it can take values 5 and 7
Hence, possible pairs are (5, 7) and (7, 9)

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