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


Let us assume x be the smaller of the two consecutive even positive integers

Other integer = x + 2


It is also given in the question that, both the integers are larger than 5


x > 5 (i)


Also, it is given in the question that sum off two integers is less than 23


x + (x + 2) < 23


2x + 2 < 23



x > 10.5 (ii)


Thus, from (i) and (ii) we have x is an even number and it can take values 6, 8 and 10


Hence, possible pairs are (6, 8), (8, 10) and (10, 12)


24
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