15. The sum of the seven digits of the number ' $a a a b b b b$ ' is equal to the two-digit number ' $a b$ '. What is the value of $a+b$ ?
A 8
B 9
C 10
D 11
E 12
15. C The value of ' $a b$ ' is $10 a+b$ so $3 a+4 b=10 a+b$ which gives $3 b=7 a$. Hence $a$ is a multiple of 3 and $b$ is a multiple of 7. Also $a$ is non-zero (as it is the leading digit), and hence $b$ also cannot be zero. The only single-digit solution of $3 b=7 a$ is $a=3$ and $b=7$, so $a+b=10$.