BJT Circuit Problem Find Vc Quickly

[theBEAST]

Homework Statement

Here is the diagram and solution for the problem:

The only problem I have is how the solution was able to find the voltage Vc so fast. They got the answer 3V without showing any work?

 

[NascentOxygen]

Were you told that VE = 7v? That means IE is 3mA. With IC practically equal to IB, that 3mA passes through the collector resistor to ground.