Critical path question

You are a principal at an architecture firm which has made you the Project Manager in charge of building four new apartment and office towers on a larger waterfront construction. The project has a critical path of twenty-three weeks. What is the impact on the duration of the critical path if the management wants you to complete the project in twenty weeks?
 
 
  Choice 1 Increases by three weeks.
 
  Choice 2 Decreases by three weeks.
 
  Choice 3 Remains the same.
 
  Choice 4 Cannot be determined.
 
 
  Correct Choice : 3
 
Justification :
  Duration of critical path = 23 weeks
If the management wants to complete the project in twenty weeks, then the project float will be: 20 - 23 = -3 weeks The project float compares the critical path with an externally imposed date and may be negative. You may be forced to fast track or perform crashing to ensure that the project is completed on time as required by the management.
 
There will be no change to the critical path. 
 
Reference: PMstudy.com comments
 
 
 
i think 2 is correct. Can somebody help to explain? thanks!
 
 
 
 
 
 
 

Justification given  by pmstudy,com is self explainatory.. What is not clear to you here ?

If you have Rita guide.. see page 227 that sure helps.
The main idea PMBOK is trying to tell us is that if the end date of the project changes the network diagram does not change automatically i.e. PM need to looks for options to compress the schedule etc.

The critical path remains as critical (network diagram)if you do crashing only.
The critical path will change, if you do FasT track.

If the critical path does not change, per pmstudy response, then the project duration remains at 23 weeks. Since the network diagram is part of the plan, hence, the project is still on target if it finishes the project in 23 weeks, is that correct? I'm just basing on the plan, the network diagram.

In my opinion the PM will do schedule compression specifically on activities within the critical path, just to meet the 20 weeks mandate. So if it is able to able to compress schedule shaving off three weeks, then the new critical path will become 20 weeks, and no longer 23 weeks, hence the impact is "decreases by three weeks". More info will be appreciated, as I'm not totally bought in on the response. Thank you.