Problem Solving

To verify that a given n-digit positive integer is divisible by 7, we perform the "Index of 3 Test" with the number; for example, to verify that 259 is divisible by 7, following way goes the "Index of 3 Test":

259 → 2 × 3^2 + 5 × 3^1 + 9 × 3^0 = 18 + 15 + 9 = 42. (Step 1)

42 → 4 × 3^1 + 2 × 3^0 = 12 + 2 = 14. (Step 2)

14 → 1 × 3^1 + 4 × 3^0 = 3 + 4 = 7. (Step 3)

It took 3 such steps to get 7 in the end, and we’re sure that 259 is divisible by 7. How many such steps are needed to be taken so as to make sure that 11116 is divisible by 7?
A. 2
B. 3
C. 4
D. 5
E. 6


MBM