Solution:

Bill. If you read the message upside down, you'll notice that the numbers resemble letters and that those letters form legible sentences. The message is 'Bill is boss. He sells oil.'

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:

A
D
C
A
B

Solution:

The answer is 'R'

It represents the gear stick. The number 1-5 represents gears and the last one thus should be reverse i.e. R.

Solution:

If the man killed himself, he would not have been able to rewind the cassette. Thus it is clear someone else killed him.

Solution:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

Solution:

146900

Explanation:
Whenever you face such type of questions, it is wise to begin from the last thing. Here in this question the last thing will be the 9th temple. He climbed down 100 steps and thus you know, he had Rs. 100 before beginning climbing down. Thus, he must have offered Rs. 100 to the god in that temple too (he offered half of the total amount). Also, he must have dropped Rs. 100 while climbing the steps of the ninth temple. This means that he had Rs. 300 before he begand climbing the steps of the ninth temple.

Now, we will calculate in the similar manner for each of the temples backwards.
Before the devotee climbed the eight temple: (300+100)*2 + 100 = 900
Before the devotee climbed the seventh temple: (900+100)*2 + 100 = 2100
Before the devotee climbed the Sixth temple: (2100+100)*2 + 100 = 4300
Before the devotee climbed the fifth temple: (4300+100)*2 + 100 = 8900
Before the devotee climbed the fourth temple: (8900+100)*2 + 100 = 18100
Before the devotee climbed the third temple: (18100+100)*2 + 100 = 36,500
Before the devotee climbed the second temple: (36500+100)*2 + 100 = 73300
Before the devotee climbed the first temple: (73300+100)*2 + 100 = 146900

Therefore, the devotee had Rs. 146900 with him initially.

Solution:

Ms. Britney did it.

We will take up every person and analyze the statements over all of them one by one.

Case 1: Ms. Britney did it, then
Statement 1 => true
Statement 2 => false (as Rihanna did not do it)
Statement 3 => false (as Ms. Britney is lying)
Statement 4 => false (as Ms. Gwyneth is lying)
Our first guess itself was right but let us confirm our analysis by analyzing the statements over others.

Case 2: Ms. Rihanna did it, then
Statement 1 => false (as Ms. Britney did not do it)
Statement 2 => true
Statement 3 => true (as Ms. Britney is not lying)
As per the conditions, three statements had to be wrong but here, we have two statements right which clearly contradict the condition.

Case 3: Ms. Gwyneth did it, then
Statement 1 => false (as Ms. Britney did not do it)
Statement 2 => false (as Ms. Rihanna did not do it)
Statement 3 => false (as Ms. Britney is lying)
Statement 4 => false (as Ms. Gwyneth is lying)
She did not do it as all the statements are false.

Case 4: Ms. Yoon did it, then
Statement 1 => false (as Ms. Britney did not do it)
Statement 2 => false (as Ms. Rihanna did not do it)
Statement 3 => false (as Ms. Britney is lying)
Statement 4 => false (as Ms. Gwyneth is lying)
All four statements are false in her case as well thus she did not do it.

Therefore we have proved that Ms. Britney did it.

Solution:

At every floor, the detective had to open the window himself. If the man had committed suicide, then at least one of the windows must have been open. A person who is committing suicide won’t close the window behind him. Thus he knows that someone pushed him off the edge and closed the window afterwards.

Solution:

Step one: First you will have to make 3 trips of 1,000 apples 333 miles. Then you will be left with 2,001 apples and 667 miles to go.

Step two: Next you will have to take 2 trips of 1,000 apples 500 miles. In this manner you will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).

Step three: At last, you will have to travel the last 167 miles with one load of 1,000 apples and you will be left with 833 apples when you reach the town

Solution:

Since each one of them gave one answer wrong, this means that each one of them gave two answers right.

Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.

Thus both Student A and Student B must be right with the first question and the answer to the first is two.

If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
Q1. Two
Q2. Three
Q3. Two