How many applicants need to apply in order to meet the hiring target? Cam needs to hire $30$ new employees. Ten percent $(10\%)$ of applicants do not meet the basic business requirements for the job, $12\%$ of the remaining applicants do not pass the pre-screening assessment, $23\%$ of those remaining applicants do not show up for the interview, and $5\%$ of those remaining applicants fail the background investigation. How many applicants need to apply in order to meet the hiring target?
$$A)\ 30\ \ \ \ \ \ B)\ 45\ \ \ \ \ \  C)\ 50\ \ \ \ \ \ D)\ 52\ \ \ \ \ \  E)\ 60$$
My answer:
I added $10+12+23+5=50$ 
That gave us $50\%$. I took a look at the answers and getting $50\%$ of $E)\ 60$ is $30.$
However, when I tried to solve it, I took $(0.50)(30)=15$ I then added $15$ to $30$ and it gave me $B)$ $45.$ Can someone please show me how to solve this?  

To elaborate on John's answer: You cannot simply add $10$, $12$, $23$, and $5$ percent, because the percentages are "in tandem".  After you cut away the first $10$ percent, you only cut away $12$ percent of those who remain, not of those who started the selection process.
As a simpler example, consider the following selection process: You first eliminate those who are born in an odd-numbered month, and then you eliminate those who are born on an odd-numbered day.  If we assume (for the sake of argument) that each step removes $50$ percent of the remaining candidates, it still is not true that at the end of the two steps, you have eliminated $50+50 = 100$ percent of the candidates.
Instead, what happens is that after the first step, $50$ percent have been eliminated, and $50$ percent remain.  The second step then eliminates $50$ percent of the remaining $50$ percent, or $25$ percent.  That leaves only the last $25$ percent.
In the same way, in your actual problem, the first step eliminates $10$ percent, leaving $90$ percent.  The second step eliminates $12$ percent of that $90$ percent, leaving $88$ percent of $90$ percent, or $79.2$ percent.  And so on.
