Which two-digit numbers are exactly equal to seven times the sum of its digits?

#### Solution

21, 42, 63, and 84.

If the number is “AB”, you can set up a simple equation: 10A + B = 7(A + B), which simplifies to A = 2B. Since A is a digit, A <= 9 by definition, so there are only four possible two-digit numbers that satisfy the condition A = 2B.