Math Riddles

Question: Two spies want to get in an enemy's military base. In order to get in they have to give the correct countersign to the guard at the gate after he gives them the sign. So, they wait hidden nearby the gate so that they will overhear the countersign from another soldier. One soldier comes and the guard gives the sign: "6". The soldier answers "3". The guard lets him pass. Another soldier comes. The guard says "12" and the soldier gives the answer "6". The guard lets him pass. So, the first spy goes at the gate and the guard says "10".The spy, sure that he knew the answer as he was, says "5". Immediately, the guard shoots him dead. Then the other spy, who saw that the other spy was killed when he gave the countersign, had now understood what the right answer would be, whatever the guard's sign was.So, he walks to the gate and the guard says "8".The spy gives the correct answer and the guard lets him in. What was the answer that the spy gave?

Question: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.

What is the fewest number of pairs you need to test to guarantee you can get the flashlight on?

Question: If you randomly choose one of the following answers to this question, what is your chance of getting it right?

A) 50%
B) 25%
C) 0%
D) 25%

Question: Which is the missing number in the below Number Series? 2, 3, 5, 7, 11, 13, ?, 19

Question: Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him "Why on Earth have you missed so many days?"

Thomas replies "There just isn't enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that's 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days.

Add all of that up and you get about 361 days. That only leaves 4 days for school."

The principal knows Thomas is full of it, but can't figure out why. Where is Thomas going wrong?