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?  

Assuming $N$ as the number of all the applicants, if we consider four groups as the fail groups, named $A,\ B,\ C,$ and $D$ as you mentioned in the question, respectively. According to your given data, the percentages of these groups are as follows. 
$$A=\frac{1}{10}\times N=0.1\times N$$ $$B=\frac{12}{100}\times(1-0.1)\times N=0.108\times N$$ $$C=\frac{23}{100}\times(1-(0.1+0.108))\times N\approx 0.205\times N$$ $$D\approx\frac{5}{100}\times(1-(0.1+0.108+0.205))\times N\approx.029\times N$$
So, the total number of failed applicants is $(0.1+0.108+0.205+0.029)N=0.442N$, and hence we have $(1-0.442)\times N\approx30$ which leads to $N\approx 53$, and so according to the options, it is concluded that $\color{red}{N=52}$.
