I doubt the havc is the culprit but it's easy to find out. At a time you don't need the unit on,cover first the inside then the outside and finally,cover both sides of the unit with movers pads,heavy blankets or quilts. I believe you will notice little if any improvement. Granted,people's voices outside your apartment often come through,but you should be used to that. I have had some but not great amount of sucess in the latter condition adding sound deadening insulation to the sleeve.

klem1 - thank you for your very helpful response. I implemented your suggestion this morning when I started hearing noises in my bedroom. You were right, muffling the PTAC didn't improve the noise, which led me to the ultimate problem - the walls. I put my ear to the walls in the bedroom and it was only one, the one with plumbing (and that likewise goes straight up and down to the other apts), through which I could hear the sounds that much more clearly. I must never had this problem in my apartments before because they were much smaller (studio, one bedroom) with far fewer of these "continuous" walls through which sound will travel. I guess I will have to start looking into soundproofing the walls..? Thank you again.

you could have an insulation company insulate the
walls. they drill a hole & pump insulation into the
cavity between studs. if your walls have fire blocking
they would have to drill top of wall & again below
fire blocking to fill entire stud bay.
holes are plugged with cap.

walls shared with other apt dwellers would have
to be insulated from inside your apt.

this would be the less expensive,intrusive option.
others would include sound board on walls or
layers of sheetrock with hat channels to
absorb sound.

best of luck.

Energy rater- Thanks very much for the advice! Do you know if it's okay to pump insulation as you suggest into walls containing plumbing and wiring? I'm assuming yes, but I don't understand why the building contractors wouldn't have done this in the first place.

only if wiring is old knob and tube would it
be an issue.
contractor was saving a few bucks by
not insulating shared walls.
even in new construction adding unfaced
batt insulation in walls shared with bathrooms
& common areas is an extra cost to homeowner.

builders/contractors build & move on. they
don't usually live in the spaces they build.

best of luck.

You said "I don't expect a solution that will block out the sound entirely, but any improvement will bring my blood pressure down."
To give you opertunity to weigh options and perhaps get estimates, you might consider putting a soft sound deadening material on the wall for now. Better desisions are made while blood pressure is in normal range. LOL
You might also place the subject on the agenda for next H.O. meeting. I would ask for 5 to 10 minutes just to see what others have done and test the waters on the overall feeling about it. Depending on what you come away with , a longer in depth discussion might be nessary to let bids on several residents for better pricing if professional help is nessary.

Energy_rater_la & klem1 - thanks to both of you again for your advice. Klem1 - do you have a suggestion for a sound deadening material to put on the walls? And would this material work for floors, too?

I spoke to the building contractors who built out the apartments and they swear the walls can't be the problem in the bedroom (where the noise is the worst) because there are no walls with pipes in this room. The bathroom is right next to the bedroom and the bathroom wall with pipes is adjacent/continuous with the bedroom wall where I could make out the voices by putting my ear to it, but THAT bedroom wall is actually a masonry wall! The sound isn't just coming from the bathroom because closing the bathroom door doesn't lessen the sound any. The contractors say maybe the sound is coming through the floors, which are hollow cement. I guess it's possible, but it's hard for me to believe that normal volume voices can travel that much through cement/cork/flooring. I am thinking of hanging the sound-deadening material on different walls and the floor to see if I can locate the source. We haven't put rugs down yet, so if the floors are the problem, maybe it's as simple a solution as this (I really hope so).

Sound deadening material I had in mind is temporary and low tech such as atractive rugs or bat filled comforter. If you carpeted the walls,I suppose the same could be used on floors but I believe you would soon tire of that.
If by contractors,you mean general contractor or subs,I wouldn't put a lot into thier opinion unless they are one in a million. If you spoke with the architectural desighner, I would consider his information golden and start looking to see where his desighn was not incorpirated. I hope this doesn't come as a shock,it's all to common for contractors to leave off costly material speced on a job to increase profit. The lite weight concrete do'es a good job that isn't fully apreciated until you spend time beneath a place that doesn't have it. If it doesn't sound like they are moveing furniture when walking upstairs,voices aren't coming through the floor.

pick a small room & put an area rug down.
see if this lessens noise transfer.

adding soft materials to absorb sound
may work. things like drapries, tapestry wall
hangings etc work well for echos in rooms
with tall ceilings.

in the one room add materials to floor
& walls, even if it isn't stuff for that room...
just to get an idea if it works or not.

it is possible that over time you'll adjust
to the noise, although it doesn't seem
that way now.

I lived for a short while in on the second
floor of an apt complex...noise from
downstairs neighbors drove me nuts
for about a month...then I got used to it.
keeping music at a low level made the
adjustment easier.

but when I lived in duplexes in N.O.
with no insulation...I'd move if neighbors
were too loud.

carpeting the walls is drastic..maybe some cork tiles?
not sure, but best of luck.

klem1 & energy_rater_la - Thank you for your follow-up advice. I wanted to respond with an update, which I now have. After some investigation, we believe the sound is coming through both the floors and walls. Perhaps even more so through the floors, but the walls are definitely not as soundproofed as the contractors claimed. At this point, our plan of action going forward is to make nice with the neighbors (they're getting noise from us, too, so it's in everyone's interest to be considerate of each other), lots of rugs (which are required by building rules), and push the contractors to pump insulation into as many walls as possible. I've decided against asking the contractors to rip up the flooring and put down better insulation (at our cost, even) as this would be like opening Pandora's box (i.e., wreaking havoc on our apt). And perhaps most importantly, we will have to learn to get used to and ignore the noise.

Thanks so much to both of you for all of your helpful advice.

hope that it all works out! & thanks for the update.

You are quite welcome pnadaroux,and thank you for the follow up. I wish more people would see their post all the way through so we know what if any good our advice was.
Too many show up,ask how to remove the tamper resistant screws from their breaker panel and that's the last we hear from them. Fot all we know,they got inside then electracuted themselves.