What does it mean?

Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

Can you find out the remainder when 3^300 is divided by 5?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, "Oh! I am really sorry, I thought this was my room."
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.

Rose, Lily and Jasmine decided to buy flowers for their moms on Mother's Day. One of them bought lilies, the other roses, and the third one jasmines.
'It's funny!' said the girl with roses, 'we bought roses, jasmines and lilies, but none of us bought the flowers matching her name'.
'You're right!', said Lily.
What kind of flowers did each of the girls buy?

What goes up but never comes down?

I come in different shapes and sizes.
Parts of me are curved, other parts are straight.
You can put me anywhere you like,
but there is only one right place for me.
What am I?

I hide my treasure in the ground, my tail is big and fluffy. If you spot me in a tree, please don’t call me scruffy. What am I?

People make me, save me, change me, raise me. What am I?

Why 1729 is a magic number? Answer Logically.