17. The six-digit number $2 P Q R S T$ is multiplied by 3 and the result is the six-digit number PQRST2. What is the sum of the digits of the original number?
A 24
B 27
C 30
D 33
E 36
Solution
B

Let the five-digit number $P Q R S T$ be $x$. The condition in the question tells us that $3(200000+x)=10 x+2$. Therefore $600000+3 x=10 x+2$ and hence $599998=7 x$. This has solution $x=85714$ and hence the sum of the digits of the original number is $2+8+5+7+1+4=27$.