What is both possible and impossible at the same time?

A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

I am not alive, but I grow; I don't have lungs, but I need air; I don't have a mouth, but water kills me. What am I?

John and his wife were living in a rural place. On a particular day, John's wife fell ill and he called the local doctor. When the doctor picked up, he said, "Doctor, my wife is ill. She might have appendicitis."

"This can't be possible! I took out her appendix two years ago myself," the doctor explained.

When diagnosed, John's wife was found to have appendicitis. How can this be possible?

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

I shave every day, but my beard stays the same. What am I?

John can fit six large chocolate boxes or nine small chocolate boxes into a carton. How many cartons will he require to put sixty-six chocolate boxes into?

There was a greenhouse.
Inside the greenhouse, there is a white house.
Inside the white house, there is a red house.
Inside the red house, there are lots of babies.

What is It?

Give it food and it will live; give it water and it will die.

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'

What are the two numbers?