Who is that with a neck and no head, two arms and no hands? What is it?

When Jack was six years old he hammered a nail into his favourite tree to mark his height. Ten years later at age sixteen, Jack returned to see how much higher the nail was. If the tree grew by five centimetres each year, how much higher would the nail be?

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?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

Different lights make me strange by changing me into different sizes. What am I?

There was once a troop of 5 elves. The 5 elves were very dedicated on finding the magical treasure of 1000 coins. However, being elves, they were super geniuses, very greedy and they did not hesitate in taking lives of other elves. The 5 elves were named Aye, Bee, Cee, Dee and Ee, ranked from high to low respectively, from Aye to Ee. One fine day, their efforts brought results and they found 1000 coins. Now they had to split it in between them as per their ranks. The lowest ranked elf has to make the proposal. If the proposal is accepted by majority, it is agreed, or the suggesting elf is killed.

What proposal should elf Ee make ?

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

Kareena is older than Katrina and younger than Karishma. Isabelle is younger than Bipasha and Karishma. Bipasha is older than Karishma. If Kareena and Isabelle are the same age, who's the youngest?

When I got four, I have it none.
When I got two, I have it some.
When I got none, I have it all.

What is it?

Our product and our sum always give the same answer. Who are we?