Hi I took the placement test a while back and here are a few problems I got confused with. Can anyone please explain these to me?

1. A five legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?

1. 6

2. 9

3. 12

4. 13

5. 15 correct answer is D

2.  Consider the number :   201720172017… 2017    where the number consists of 2017 copies of the digits 2017. What is the remainder when this number is divided by 11?

(for this problem i just want to know if there is an easy way to do it. The correct answer is 5.)

3. Suppose you have one copy of each of the 7 different Harry Potter books. You give out all to 3 of you friends. Each friend gets at least one book. How many ways can you give out the books? (The books to 3 of your friends are not in any specific order).

The correct answer is 21)

4. Spinners A and B are spun. On each spinner the arrow is equally likely to land on each number. What is the probability that the product of the two spinners’ numbers is even?

1. ¼

2. ⅓

3. ½

4. ⅔

5. ¾

5. Consider the integer solutions to (x^2 + 4x + 8) ^2 + 3x ( x^2 +4x+ 8) +2(x^2) = 0. What is the product of all the integer solutions?

The correct answer is 8.

6. Steve as 6 different bars of candy. He wasn’t to bring the candy to eat during lunch the next three days (2 candy bars each day). How many different ways can Steve divide his candy bars into 3 groups to bring to lunch?

The correct answer is 90.