Q. 405.0( 1 Vote )

Find all pairs of consecutive even positive integers both of

which are larger than 8 such that their sum is less than 25.

Answer :

Let the pair of consecutive even positive integers be x and x + 2.


So, it is given that both the integers are greater than 8


Therefore,


x > 8 and x + 2 > 8


When,


x + 2 > 8


Subtracting 2 from both the sides in above equation


x + 2 – 2 > 8 – 2


x > 6


Since x > 8 and x > 6


Therefore,


x > 8


It is also given that sum of both the integers is less than 25


Therefore,


x + (x + 2) < 25


x + x + 2 < 25


2x + 2 < 25


Subtracting 2 from both the sides in above equation


2x + 2 – 2 < 25 – 2


2x < 23


Dividing both the sides by 2 in above equation



x < 11.5


Since x > 8 and x < 11.5


So, the only possible value of x can be 10


Therefore, x + 2 = 10 + 2 = 12


Thus, the required possible pair is (10, 12).


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