Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
A. 3
B. 6
C. 9
D. 12
E. 15
If two sets of four consecutive integers have one integer in common, the total in the combined set is 7 and we can write the sets as
n + (n + 1) + (n + 2) + (n + 3 ) and
(n + 3) + (n + 4) + (n + 5) + (n + 6)
Each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12.