$35=5\times 7$  $84=2\times 2\times 3\times 7$  Because $B$ is the factor both number contains, $B=7$  Thus, $A=5$, $C=12$. 
There are three whole numbers $A$, $B$ and $C$. $A\times B=35$, $B\times C=84$. $A+B+C=$~\uline{~~~~~~~~~~}~. 

[A] $$20$$ 
[B] $$23$$ 
[C] $$24$$ 
[D] $$29$$ 