Explanation
Even number is defined as those integers which are divisible by 2. Therefore consecutive integers are for example : 2, 4, 6, 8,.... As you can see the one of the basic properties of even numbers is that
when an even number is subtracted from another even number the result will be an even number.
So we can write given k,j are even integers and k>j:
k = j + 2n, where n is an integer.
However it must be noted n doesn't represent the number of integers between k and j. There is a counting problem there. The number of even integers between k and j is (n-1).
Foe example if we check the concept to determine the number of even numbers between say 2 and 8. We can easily determine that there are only two namely, 4 and 6.
8 = 2 + 2 *3 (k = j+ 2n)
In this particular case n = 3. So the number of even integers between k and j is
n-1 where n = \(\frac{(k-j)}{2}\). Therefore n-1 = \(\frac{(k-j - 2)}{2}\). The correct choice is A.
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