I am an odd number. Take away a letter and I become even. What number am I?

Can you name four days which start with the letter 'T'?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

Replace the question mark with the correct number.

John went to a parrot shop in Mexico, and the parrot owner told him that his parrot is so unique that he repeats everything he hears. John got excited and immediately bought the parrot. John went home and spoke many words, but the parrot does not repeat anything.
He went again to the parrot shop and complaint to the shopkeeper, but the shopkeeper never lied. Explain?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.