This would work well.

Not sure what kind of door it is, but after the Newtown shooting, literally dozens of door blocks came out for classrooms. They are made to cheaply and easily prevent a door from being forced in an emergency, so I think they'd be perfect in this situation. Dr. Google will be your friend.

millorkman's suggestion is good, particularly if someone is pretty basic in handyman skills as it's surface mounted and would not involve drilling the door for another cylinder. Alternatively, you could just remove the existing deadbolt and buy a new one as the setbacks are pretty standard. When you say the deadbolt is "loose," what exactly does that mean?

The best I've seen is called"Texas Security Bolt". The Home Depot # is U-9493 in white and U-9494 in brass but you can find it elsewhere under different # and same name. Simple as falling off a log to install and will not budge even if the door is kicked into splinters. Never requires adjustment regardless how bad buildings settle or move. Remove it at move out and door is unscarred.

Check with the manager or owner first before installing a new lock on a rented apartment's door

Anything permanently installed should be approved by the management.

I'd suggest a cheap stick-on magnetic door alarm.
Example

It won't prevent someone from breaking in, but they won't do it quietly!

Klem-

I agree. I've lived in number of apartments where the door hardware was really crappy and I put in my own. In this situation, the rule that applies is that it's easier to be forgiven then get permission.

the deadbolt was loose when the kids moved in which proves neglect

It's only neglect if the issue was brought to their attention and they didn't do anything. And "a little loose" is open to a lot of interpretation. It might be perfectly fine (or it might not).
A rental property owner would have to be an idiot to expose themselves
to liability posed by refusing to alow tenant to secure the door as well
as possible.

As well as possible? No. Adequately? Yes.

And since they shouldn't be refused, why not ask before installing it? Then there's no way they'll get dinged on their security deposit when they move out.

And the management might even buy and install it if you bring it to their attention. There's really no downside to asking permission.

Bottom line is that you shouldn't be making any permanent modifications to a place that you're renting. It isn't YOUR property.

I have something called Add-a-lock. Sorry I can't link but it's easy to find online. It's a portable lock you slide into the strikeplate as you close the door. It's incredibly strong and easy to use - it would be perfect for them.

Has anyone tried this?

http://www.amazon.com/Master-Lock-265DCCSEN-Dual-Function-Security/dp/B0002YUX8I/ref=pd_sim_469_3?ie=UTF8&refRID=0EXMC7T62KJHJ6TNG4BR&dpID=216GN31N30L&dpSrc=sims&preST=AC_UL160_SR160%2C160

"Why would they refuse?" is the wrong question. If nothing else you should get permission just to avoid losing your security deposit when you leave holes in the door. Or, be prepared to fill them (properly, not with toothpaste) when you leave. How would you feel if that was your rental property? Just be a good neighbor.

It's your call though, we haven't met the mgmt. or creepy maintenance guy.

These young women should have firearms training and a pistol. I'd recommend the Judge.

Joseph- Let's not go down that road...

To kudzu9:

What do you have against women protecting themselves? I am 67, live alone except for the dogs and have 2 guns; both loaded and ready to go at all times. Well, they are ready to chamber one and then ready to fire. If someone is fool enough to think they can get by the dogs, they will be met with 00 buckshot if they are threatening me and my safety.

There are too many crazy people in the world to not be responsible about your own safety.

gardenerlorisc-

Some people don't see more guns in this country as a solution, and the fact that a simple request for advice on improving a lock elicits an exhortation to get a gun is deeply troubling. I'm a father of three girls who was always concerned about their safety, so please don't jump to conclusions about my views on women protecting themselves. I just never thought that putting guns in their hands would improve their lives. You're entitled to do what you like. I'm not going to debate you.

Fair enough, but what is the subject of this thread? Is it purely a technical question on locks, or is it a larger question of security?

I have a history of providing sometimes contrarian step-back-and-look-at-the-bigger-picture type of advice. That's what I've done here and will continue to do.

To Kudzu9

Doesn't matter to me.

Better to have it and not need it then to need it and not have it.

"Better to be tried by 12 than carried by 6."