If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E…
If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?
9
8
7
Cannot be determined due to insufficient data
Solution
Adding two-digit numbers AB + CD gives the three-digit number 1CE. The tens column gives A + C (plus any carry) = 1C, i.e. equals 10 + C. Case with no carry from units: $A + C = 10 + C$ gives $A = 10$, impossible. Case with carry 1 from units: $A + C + 1 = 10 + C$ gives $A = 9$. Hence A = 9.