25. How many three-digit numbers are equal to 34 times the sum of their digits?
A 0
B 1
C 2
D 3
E 4
25. E Let the three-digit number be $100 a+10 b+c$. Since each suitable number is 34 times the sum of its digits, we have $100 a+10 b+c=34(a+b+c)$. Therefore $66 a-33 c=24 b$. Since the left-hand side of this equation is a multiple of 11 , the righthand side is also a multiple of 11 and hence $b=0$. Therefore $66 a-33 c=0$ and hence $c=2 a$. Therefore the three-digit numbers with the required property are $102,204,306$ and 408 and hence there are four three-digit numbers with the required property.