Mean & Median of consecutive integers are same. Since we know the median and since we know that all integers are consecutive, we can add 2 to 2k-1 to get the highest number and deduct 2 from 2k-1 to get the lowest number. Based on this, we can get the difference.

HTH

Whenever I am faced with consecutive integer problems, I tend to take 'n' as the middle term which gives me the series as n-2, n-1, n, n+1, n+2. (e.g. 3-2, 3-1, 3, 3+1, 3+2)

Thus the difference between the highest and the lowest integers will be n+2 - (n-2) = n+2-n+2 = 4 (irrespective of the actual number)

Hope this helps,
Vivek

Isn't it a questions more simple than it looks?
five consecutive integers
difference between greatest and least is always 4
no need to solve 2k-1
Is this GMAT problem?

Def. sleep deprived when I was doing the question
Sorry got thrown off by the negative integer thing