The problem description is this:
In a survey of $190$ manufacturing companies, $103$ hired operators, $67$ hired technicians, and $49$ hired both operators and technicians, as illustrated in the Venn diagram below:
How many companies surveyed have hired at least one category of employees: operators and technicians?
First of all what I have tried is to understand how much operators and technicians were without having both professions, so I have added $103 + 67 = 170$; then $170 + 49 = 219$, so finally $219 - 190 = 29$. So now what should I do? If we note that $29$ are both, then we can see that only operators are $103 - 29 = 74$ and only technicans are $67 - 29 = 38$, is it right? But what about question itself? If I add both results, I get $74 + 38 = 112$, but in answer there is $121$ as correct answer, what is worng?