I have branches, but no fruit, trunk or leaves. What am I?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet.

How many miles does the pigeon travel?

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

A new Engineering building containing 100 offices had just been completed. John was hired to paint the numbers 1 to 100 on the doors. How many times will John have to paint the number nine (9)?

You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles, and 2 empty bowls. He then says, 'Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK... you will die.'

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

Can you make a six-letter word using the letters N, A and B ?