Solution:

I have three theories based on which it can be either Murder, Suicide, or Accident.

Case1 : Its a Murder
Reason1: If it's suicide then a person must have waited for the Cigarette to end.
Reason2: Blood is spattered on the right side and the pistol is also on the right side. which seems pistol is planted at the end.

Case2 : Its a Suicide
Reason1. The lamp was switched off and glasses were removed which indicates she done writing(probably suicide note). The murderer does not care about switching off glasses or removing glasses.
Reason2: The blood was just on the wall at the height of a person. If it's a murder the blood must have been scattering around.
Reason3: Burning cigarette and alcohol indicated depression level which often is the reason for suicide.

Case3 : Its a Accident
It's must be an accident. The girl was writing using the pen and suddenly she heard a sound. She must have a gun for safety which she takes out of the security. As a preventive measure, she switched off the light so that she can't be seen in the dark. Also removed the glasses as they are of no use in the dark. After a while, she realized that it's just a sound. So to calm her down she drinks and also lights a cigarette. suddenly she slipped and try to hold stool but failed and forced her head into the wall and died.

Solution:

Since Jasmine and Thibault ate equal amount, they should pay the same amount. But since that's not possible, they can decide with 'rock, paper, scissor' or an equivalent measure to determine who will pay the extra dollar. Now, let's assume tha Jasmine pays $1 extra after losing

Jasmine will pay $5, Thibault will pay $4 and Noah will pay $2.

If the pizza's cost was $11, we can simply keep the same offset and divide. Jasmine is paying 6% more, Thibault is paying 15% more and Noah is paying 27% more.
Keeping the offset same both Jasmine and Thibault will pay $5 each and Noah will pay $1.

Solution:

One of the cop will move clockwise while the other will move anti-clockwise every day. In such a manner, they will catch the thief in minimum seven days.

Solution:

To do it, the marbles must be arranged as the vertices of an octahedron. If you are unsure, check the image below.

Solution:

Yes it is possible in Roman Numerals. In Roman Numerals,
9 = IX
10 = X
11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.

Solution:

At each draw, the number of strawberry candies are either decreasing by 2 or not decreasing at all. In the case of orange candies, at each draw, they are either increasing by 1 or decreasing by 1.

Thus on an assumed outset with at least one candy in the jar to begin with, if the number of strawberry candies are 0 or are even in numbers, they will finish off leaving an orange candy at the end. If otherwise, the remaining candy will be a strawberry one.

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:

30,450 miles.

Explanation:
For each 5 miles driven using this rotation, each tire will lose (2/29000)+(2/21000) of its tread.So, suppose we drive 5*N miles like this. Then, each tire will lose 2*N*((1/29000)+(1/21000)) of its tread. We wish to determine N so that the latter expression gets to be 1, representing all of each tire's tread. That happens when N=6090, which is when 5*N (the total miles driven) is 30,450.

Solution:

XIX is the answer which refers to nineteen in roman numeric system. On taking out one i.e. I, we will get XX that is equal to twenty.

Solution:

It will take the man 58 minutes to reach the top.

Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute.
Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back.

Solution:

The answer is very simple. All she had to do is take the fifteen cards from the top and reverse them. This would make another pile out of that and there will be two piles - one of 15 cards and one of 37 cards. Also both of them will have the same number of inverted cards.

Just think about it and if the mathematical explanation will help you understand better, here it is.
Assume that there were p inverted cards initially in the top 15 cards. Then the remaining 37 cards will hold 15-p inverted cards.
Now when she reverses the 15 cards on the top, the number of inverted cards will become 15-p and thus the number of inverted cards in both of the piles will become same.