Solution:

3

Explanation:
Fernando + Alonso + McLaren = 6
Fernando x Alonso = 2
Alonso x McLaren = 6

Given.
Fernando x Alonso = 2
Alonso x McLaren = 6

Rewriting Both equations in terms of Alonso,
Fernando = 2/Alonso
McLaren = 6/Alonso

Replacing above values in equation "Fernando + Alonso + McLaren = 6"
2/Alonso + Alonso + 6/Alonso =6
(2 + Alonso^2 + 6)/Alonso = 6
8 + Alonso^2 = 6Alonso
Alonso^2 - 6Alonso + 8 = 0
(Alonso - 4) (Alonso - 2) = 0

Therefore;
Alonso = 4 or 2

Let's take value of Alonso as 2
Fernando = 2/2 = 1
McLaren = 6/2 = 3

Therefore;
McLaren x Fernando = 3 x 1 = 3

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

Solution:

Yes, some people are going get really tiny pieces but you were allowed for that right. Also, there is another way of doing it. Can you think of it?

Solution:

See the figure for the answer. Wasn't it a bit tricky?

Solution:

The Lady sitting in the chair has the detector attached to the back of her blouse.

Solution:

If you notice the animated gif, you know that D, C and B are going to die. D dies directly after coming in contact with the object, C dies after being thrust by the spikes of the see-saw and B dies with the blue ball.

But consider the situation that the person at E stands for Ebola. Eventually A dies as well.

We thank 9gags for this awesome gif.

Solution:

3/7

Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.

Solution:

The teacher will use a simple trick to form a perfect impression. He will ask all his students to raise their hands on each of the question that is asked. But the only catch will be that those who knows the answer correctly will raise their right hand and others will raise their left hand.

In this way, the principal will see all the hands being raised for each question even though all won't be knowing the correct answer. The teacher will ask only those who know the answer and they will always be correct. So the principal will be impressed to full extent.

Solution:

23rd day

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 = 276

Thus our anniversary falls on the 23rd day of the month.

You can apply other formulas to shorten the process but that is the simplest way to do it.

Solution:

Jeff Killed Mike

1. Jack is not the murderer, because he is the brother of the murderer.
2. Dan can't be the murderer since he ran a marathon, and the murderer recently had his leg amputated, and wouldn't be running a marathon of any magnitude that quickly.
3. Ben is not the murderer if he just met Jack, since Jack and the murderer grew up together.
4. This leaves Jeff and Mike.

Since Jeff is still alive (he wants to install a new computer next week, present tense) he must be the murderer. Mike also didn't grow up with Jack. It has been determined that Jack, Dan and Jeff are all alive. Ben must also be alive since Jeff plans to install Ben's computer next week. This means that Jeff killed Mike.

Solution:

There is no mention if you can use sign or not and thus the only possible way to get this is as follows:

(15 - 9) + (13 - 7) + (7 - 1) + (9 - 1) + (13 - 9)

If you solve inside the brackets, you will get the following equation
6 + 6 + 6 + 8 + 4
Adding all these numbers, you will get 30 which is the required sum.