Question

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

Answer 1

6 & 8; 8&10;10&12
These are all possible pairs of consecutive even integers which are greater than five but have a sum less than twenty three

Answer 2

$\mathtt{\huge{ \fbox{SOLUTION :}}}$

Let , x be the first even natural number , so that the other one is x + 2

The positive even integers are greater than 5 , so,

x > 5 ----- (I)

x + 2 > 5 i.e x < 3 ----- (II)

And

The sum of both numbers is less than 23 , so ,

x + (x + 2) < 23

2x < 21

x < 10.5 -------- (III)

From (I) and (III), we get

5 < x < 10.5

Since , x is an even numbers , x can take the values 6 , 8 and 10

Hence , the required possible pairs will be (6,8) , (8,10) and (10,12)