A number is even and has 10 digits, and the sum of these digits is 89. What is the unit digit of this number?
A) 0
B) 2
C) 4
D) 6
E) 8
Solution

## Alternative E

The greatest possible sum of ten digits is $10 \times 9=90$, which occurs when we have ten digits 9. To get a sum of 89, we just need to reduce one unit from one of the digits, that is, replace a 9 with an 8. Therefore, the number has nine digits 9 and one digit 8. Since it is even, its units digit can only be 8, that is, the number is 9999999998.