I live in an apartment, my bath sink won't drain completely. The drain isn't slow it just never drains completely. The standing water becomes slimy if not cleaned every day. I think there must be some design flaw in the sink itself. I'm also concerned that the slimy water is a health issue.
This is typically caused by too shallow a slope from the p-trap back to the 'Y' . That pipe is called a dirty lateral, because it fills up with gunk instead of flowing downstream to the main.
If you can open the cabinet below the sink and look back to the wall, the P-trap loop should be higher than where drain line exits into the wall. (Makes sense that the water should flow down, then loop, then out with a gentle slope, right?)
If the p-trap is too low, water rests in the drain lateral, and could back up....you can raise the p-trap to get better flow out.
If the p-trap is already above the wall exit, then I would clean out the sink tail piece as follows:
Sop up extra liquid in the sink, empty the cabinet, put down junk towels, and remove the p-trap...holding it upright to not spill as you go pour it into the toilet. With the trap removed, you should be able to shine a flashlight down from the sink bowl and see a whistle clean tube.
Duh, don't turn on any water while the sink is inn this condition.
If the stopper is in the way, remove it by disconnecting it from the control (usually with a squeeze friction clamp on the control level.) Once the stopper is out of the way, you can clean the inside of the tail piece with a small disposable rag and a coat hanger...just don't use too big of a rag and get it stuck.
After it is clean, reassemble the stopper, control lever assembly, and put the ptrap back onto the sink tail piece. All the plastic threads/fittings should be hand tight, no need to wrench them and risk cracking them.