A recruiting firm advertised for a job and people from 36 States and a Territory applied. The recruiting firm was tasked to recruit at least 25% of people from at least two thirds of the States and the Territory. If there are 100 people in each of the States and 120 people from the Territory, what's the minimum number of people the firm should at least employ?
A. 600 B. 620 C. 625 D. 630 E. None of the Above
The solution to this problem might actually be a solution to a country’s constitutional problem.
Indeed a wording problem.
Reading 1: A quarter of two thirds of $(S+t)$
You have $37$ regions, and with at least $\frac{2}{3}$ of them to be chosen from, the firm has to recruit at least a quarter of appliers from $25$ regions. These can be $25$ appliers from $25$ States each, with no applier chosen from the territory. The firm recruits a minimized total of $625$ appliers.
The formula here is $\lceil \frac{2}{3}\times 37 \rceil \times (\frac{1}{4}\times 100)=25\times 25$
$=625$ appliers.
Reading 2: A quarter of two thirds of $S$ and a quarter of $t$
You have $36$ States (from at least $\frac{2}{3}$ of which appliers are chosen) as well as $1$ territory where to recruit its quarter from. Here, the firm recruits $25$ appliers from $24$ States, and $30$ appliers from the territory, which is a total of $630$ appliers.
The formula here is $[(\frac{2}{3}\times 36) \times (\frac{1}{4}\times 100)]+(\frac{1}{4}\times 120)=[(24\times 25)]+30$
$=630$ appliers.
This goes to show how useful of a concept brackets are.