Here's the problem: A fire hose held near the ground shoots water at a speed of 6.5 m/s. At which angles should the nozzle point in order that the water will land 2.0 m. away ?
It depends on what type of alarm you're talking about. The most common types (that I've seen) are a basic form of RFID. These are the ones attached to most clothing items and on the inside of many dvd cases. A magnet MAY disable some of these items but won't set off the gates that you must pass through when entering the store.
Where do you live? In Texas, you only need smoke detectors outside bedrooms. If both bedrooms are within the same hallway, you only need one smoke detector. If they are at opposite ends of the apartment, then code will require two working detectors. If your landlord has promised to fix the broken one and has not done so yet, contact your city's Fire Marshal or building code director.