What is harder to catch the faster you run?

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.

Which is the smallest number that you can write using all the vowels exactly once?

Do You See It?

A B C D E F G H

These are the letters given to you. Now you have to find out the letter that comes two to the right of the letter which is immediately to the left of the letter that comes three to the right of the letter that comes midway between the letter two to the left of the letter C and the letter immediately to the right of the letter F.

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

Can you find the missing number in the third row?
35 20 14
27 12 18
5 2 ?

John speaks the truth only once a day in a week. Below are a few hints for you:

First: Days are Sunday, Monday and so on.
Second: One day he says, "I lie on Monday and Tuesday".
Third: On the next day, he says, "Today is either Thursday, Saturday or Sunday".
Fourth: On the next day, he says, "I lie on Wednesday and Friday".

Can you identify the day on which he speaks the truth?

Can you find the odd number in the following five choices?

1) 482636
2) 259807
3) 865195
4) 104739
5) 391744