A1. Which digit of the 7-digit number 2345678 must be deleted so that the resulting 6-digit number is divisible by 9?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
A1. A natural number is divisible by 9 if and only if the sum of its digits is divisible by 9. Since the sum of the digits of the 7-digit number 2345678 is $35=3 \cdot 9+8$, we must delete the digit 8. This gives us the 6-digit number 234567, whose sum of digits is $27=3 \cdot 9$, and is therefore divisible by 9.