
However you answer, you will be left either dead, disfigured or both... unless you can find a way to confuse her.
A Horrific Urban Legend

The young person turns off a main road and into a smaller street, the sounds of the evening traffic as people return home from work and other daytime activities grows hollow and distant.
There is noone on this new street except for a woman, a little ahead. Instantly visible is the surgical mask covering her nose and mouth, not too unusual in this part of the world with the heavy smog and a fear of airborne illnesses. The woman continues to walk towards the young person, at first looking to walk past, but at the last minute, veering to stand directly in front of them.
"Am I beautiful?" the masked woman asks.
The young person looks her up and down. She has long dark hair that passes over her forehead to partially cover her eyes, but even the jet black cannot cover the piercing brilliance of eyes that can only be described as beautiful, although quite intense at the same time.
"Yes you are." replies the young person.

"How about now?"
The young person is in shock, what stands before them is a disgusting grin. The womans mouth has been cut, the corners extended from ear to ear. The full set of her teeth are easily visible through the cut flesh, the mouth in a permanent smile.
"ye.. yes" The young person is shocked, the answer is stammered, they are unable to think.
The person they have just met is the slit mouthed woman. The young person has heard the stories told at their school. They turn to run, but after only a few footsteps, she stands before them once again, a sharp implement in her hands – scissors, a knife?

So goes the story of the Slit Mouthed Woman, known as "Kuchisake-onna" in the legend's native Japan. The legend is quite old, but noone is entirely certain when it began. What we do know however is that it came to prominence in the late 1970's, when sightings were rumored to take place around Nagasaki Prefecture, Kyushu.
The young person in the above story was possibly considered to be lucky, as they will have likely survived their wounds, though albeit with hideous scarring. It can go quite worse according to the legend.
Should they have responded 'no', when first asked if the woman was beautiful, she would have killed them there and then. The same fate would have also befallen them if they answered the same after her true face was revealed, though some legend states the young person would have been cut completely in two.
Spread Like Wild Fire
Schools organised students to walk home in groups as much as possible, as Kuchisake-onna was said to generally only prey on those alone. Students were also said to have devised a tactic to fool the slit mouthed woman, answer her questions with other questions, or do not provide a definitive answer.
Some told how she let them go after they said they had another engagement to attend to, obviously she is not immune to good manners.
The stories died down in Japan, only to surface in South Korea through the 90's.
As for who she is? Well there are a number of 'origin' tales for this legend. Some put her as a beautiful woman who was quite vain. Her husband began to suspect that she was having an affair with another man. One evening, when his paranoia got the better of him, he attacked her, slicing open her smile so that no other man would ever find her desirable.
Another story tells how in the early 70's she was a woman who used to chase and terrify children. When complaints were made against her, and the police tracked her down, she ran into heavy traffic where she was struck and died, one of her injuries - the signature slit faced smile. This particular origin is said to be backed up by a coroners findings, however, this too is probably just legend.
This urban legend is just plain creepy, how much truth there is to it is up to you to decide.
(All images are stills from the horror movies that depict this legend)