TITLE: How many applicants need to apply in order to meet the hiring target?
QUESTION [5 upvotes]: 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?

REPLY [2 votes]: If you have studied successive discounts,
the question is exactly equivalent to finding the whole dollar marked price of something
that is sold for $\$30$ at successive discounts of $10\%, 12\%, 23\%\; and\; 5\%$ 
$N(1-0.1)(1-0.12)(1-0.23)(1-0.05) = 30\; \Rightarrow N = 52$