Is it possible for young people in their 20s or 30s to get alzheimer's disease?

Yes: Less likely though. Other causes or diseases have to be considered.

Very unlikely: Alzheimer's disease is not the only cause of dementia the typical Alzheimer's disease is highly unlikely in the age group you mention.

Possible not likely: It would be very unusual for someone in his/her 20s or 30s to get Alzheimer's disease. However, there are many reasons for memory issues in someone that age--vitamin deficiency, alcohol, hypothyroidism, head trauma, drugs (Rx or other), etc. If you are worried, I would talk with your primary or go to a neurologist. Take care and stay healthy!