Solution:

In such questions, the best thing is to assume each one of them as his sister till you can find all the conditions fulfilled. According to our assumptions, Megan is Alex's sister. We will discuss only this case therefore.

Assuming that Megan is Alex's sister, she has told a lie. This also means that Maggie is not Alex's girlfriend.
If Katie is the truth speaking girl, Megan is lying and it proves our assumption.
Now, if Charlize is Alex's girlfriend, she has also told a lie. This further tells that Katie is speaking the truth which also supports our assumption.
Maggie stated that Charlize is not his sister and that is also true because according to our assumption, Charlize is his girlfriend.

Taking that into account, we can conclude that Megan is Alex's sister and Charlize is his girlfriend.

In any other assumption, you will find the data conflicting with the conditions.

Solution:

Everyone will done one day or other.

Abraham Lincoln era is too old and we expect most of them(if not all) to be dead by now.

Solution:

The probability of two numbers being relatively prime is 60%. Thus if you keep playing the bet, you will hypothetically make 20 cents on every play.

Thus, you should accept the bet.

Solution:

9

Explanation:
2 < 3 < 5
To find out the required number of candies, take one in place of the least number (i.e. take one mango candy) and then add all the greater numbers (i.e. three strawberry and five pineapple candies) to it.

Required number of balls = 1 + 3 + 5 = 9.

Solution:

Yes, you should switch the envelope. In the beginning when you picked up the envelope, you had a 1/3 probability of finding an offer letter in the envelope. There was 2/3 chance that the letter was there in the two envelopes on the table.

If you keep your selected envelope, you still have a 1/3 chance of finding an offer letter in that. However, since the interviewer has removed one empty envelope from the table, if you switch, you have a probability of 2/3 that the offer letter is inside that.

Solution:

Are you Thorgan

Explanation:
Below will be the reply of three brothers:
Eden: No (speaks truth)
Thorgan: No (speaks lie)
Kylian: Yes (speaks lie)

Therefore if its Kylian then only you will get a reply as "Yes" and then you ask for your money.

Solution:

He should shoot at the ground.

If Kangwa shoots the ground, it is Rafael's turn. Rafael would rather shoot at Ferdinand than Kangwa, because he is better.
If Rafael kills Ferdinand, it is just Kangwa and Rafael left, giving Kangwa a fair chance of winning.
If Rafael does not kill Ferdinand, it is Ferdinand's turn. He would rather shoot at Rafael and will definitely kill him. Even though it is now Kangwa against Ferdinand, Kangwa has a better chance of winning than before.

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

Solution:

This can be done if you draw a five pointed star and place the balls on the corners and intersection points. See the figure to understand better.

Solution:

For this answer is 3^0, 3^1, 3^2... That is 1,3,9,27,81,243 and 729.