We must have E = 4, since that would make a 3 • 2ABCDE end in a 2. There are no other multiples of 3n (where n is taken from {0, 1, 2, …, 9}) such that 3n ends in a 2.
So we have
3 • 2ABCD4 = ABCD42
which means 3D + 1 = 4 and so D = 1.
Then
3 • 2ABC14 = ABC142
and so 3C ends in 1. By the same reasoning as we used to determine E, we only have one possibility of C = 7, since 3 • 7 = 21 is the only multiple 3n that ends in 1.
Then
3 • 2AB714 = AB7142
which means 3B + 2 = 7 and so 3B ends in a 5. This happens if B = 5.
Then
3 • 2A5714 = A57142
which means 3A + 1 = 5 and so 3A ends in a 4. This happens if A = 8.
So we end up with
3 • 285714 = 857142
and the sum of the digits is
2 + 8 + 5 + 7 + 1 + 4 = 27
Answer:
You can also find the answer on the the Kangaroo website.
Step-by-step explanation:
