Is it possible to lose 25 pounds in a week?

Lose Slowly. Mostly like no. It is not safe to lose large amount of weight too quickly. Most of the "weight" lost would not be fat but water, which could lead to dehydration. The safest way to lose and keep weight off is to do so slowly through creating a healthy life style, not doing a crash diet. Crash diets may seem to work in the short term, but can have negative effects on your body in the long term.
Unlikely. This could only happens if you are extremely fluid overloaded and was given potent diuretics to get rid of it (water weight). From a fat weight point of view, most experts agree that it takes 3500 kcal deficit/week to lose 1 pound. This means you will have to obtain close to 100, 000 kcal deficit to lose 25 lbs. I would say chance of this happening is unlikely.