MathDB

An organization has

30

employees,

20

of whom have a brand A computer while the other

10

have a brand B computer. For security, the computers can only be connected to each other and only by cables. The cables can only connect a brand A computer to a brand B computer. Employees can communicate with each other if their computers are directly connected by a cable or by relaying messages through a series of connected computers. Initially, no computer is connected to any other. A technician arbitrarily selects one computer of each brand and installs a cable between them, provided there is not already a cable between that pair. The technician stops once every employee can communicate with each other. What is the maximum possible number of cables used?

<span class='latex-bold'>(A)</span>\ 190 \qquad<span class='latex-bold'>(B)</span>\ 191 \qquad<span class='latex-bold'>(C)</span>\ 192 \qquad<span class='latex-bold'>(D)</span>\ 195 \qquad<span class='latex-bold'>(E)</span>\ 196

Problem Statement