Solution:

There are 24 squares in this picture.

Solution:

The total number of students is 500.

To follow how and why, please see the venn diagram.

Solution:

We colored the squares in the center. They are a total of 6. If you count the ones outside it, you will find 12 squares.

6 + 12 = 18.

Therefore, there are a total of 18 squares.

Solution:

The best way to increase the probability of winning is to place one yellow ball in the first bowl and all the other balls in the second bowl.

Now, you have a 1/2 probability of choosing the bowl with just one yellow ball. If you choose that, you win.

If you choose the other bowl, it has 49 yellow balls and 50 white balls. You still have almost 1/2 probability of picking a yellow ball out of it and winning.

Solution:

17

Explanation:
Let us begin with the small square. Let us assume that their size is 1 inch.

Now, number of 1 inched squares = 12 (make sure that you don't count the 4 squares in middle twice.)
Number of 2 inched squares (double size) = 5.

Therefore, total squares = 12 + 5 = 17.

Solution:

2nd

When the cylinder is spun for the first and last time, the following six outcomes are possible:

First:
First chamber is fired first. The first player loses.

Second:
Second chamber is fired first. The first player loses.

Third:
Third chamber is fired first. The first player loses.

Fourth:
Fourth chamber is fired first. The second player loses. (First shot, player 1, chamber 4 empty. Second shot player 2, chamber 5, empty. Third shot player 1, chamber 6 empty. Fourth shot player 2, chamber 1 not empty.)

Fifth:
Fifth chamber is fired first. The first player loses. (First shot, player 1, chamber 5 empty. Second shot player 2, chamber 6, empty. Third shot player 1, chamber 1 not empty.)

Sixth:
Sixth chamber is fired first. The second player loses. (First shot, player 1, chamber 6 empty. Second shot, player 2, chamber 1, not empty)

Thus, if you analyze, you will find that the second player has a 4/6 chance of winning. Therefore if you want to win the game, going second gives you better shot at it.

Solution:

Both S and T are of same height because they are the same people.

Suppose that each person is marked with their respective number which also denotes their height.
Now when the longest from each row is called out, they will be 50, 100, 150 ... 500. Shortest among them will be 50 aka S.
When the shortest from each colum is called out, they will be 1, 2, 3, ....50. Longest among them will be 50 aka T.

Thus, they both are same person.

Solution:

16 (5 + 1 + 1 + 4 + 5)

black coloured squares : 5
red coloured square : 1
blue coloured square : 1
small green coloured squares in middle : 4
large green coloured squares : 5

Solution:

Up to a point

Solution:

75km

Explanation:
Distance between Bill and Darren = 40 km
Distance between Bill and Chris + Distance between Chris and Darren = 40 km
Distance between Bill and Chris + (Distance between Bill and Chris - 10) = 40 km
2 * Distance between Bill and Chris = 50 km
Distance between Bill and Chris = 25
Distance between Chris and Darren = 15 km

Therefore, distance between Darren's house and Alex's house = 60 + 15 = 75 km.

Solution:

The required word is BANANA.

Solution:

The man asked the king that he wanted to die of old age.

Solution:

There is a simple logic to solve this question.
The size of the chocolate is 2 x 8. Thus, you need to have 2 x 8 = 16 pieces.
Every time you break the chocolate, you will get one extra piece.
Thus, to get 16 pieces, you must break it (16 - 1) = 15 times.

Solution:

19

Explanation:
The children can purchase 19 chocolates in return.

Out of 77 wrappers, 75 will be used to buy 15 chocolates and two will be left spare.
The 15 chocolates will create 15 empty wrappers that can be exchanged to get three chocolates.
Three chocolates will return three wrappers which will help them buy another chocolate.
Now the wrapper from this chocolate and the two spare that were left earlier will get them another chocolate.
15 + 3 + 1 = 19

Solution:

Let us add the digits:
2 + 7 + 1 + 6 = 16
4 + 1 + 3 + 5 = 13
5 + 3 + 2 + 1 = 11
7 + 1 + 4 + 5 = 17

As you can see, only 2716 is a number whose digits add up to be a non prime number. Thus it is the odd one out.

Solution:

Like there is no tomorrow.

Solution:

The time at first observation:
1:12

The time at second observation:
3:24

Thus, two hours and twelve minutes have passed between the two observations.

Solution:

The probability is certain.
The average number of arms is less than 2.

Solution:

Ted will choose Ann.

You can know why after replacing each letter with the number corresponding to that letter (A = 1, B = 2, C = 3... etc.)

TED = 20 + 5 + 4 = 29
ANN = 1 + 14 + 14 = 29

If you calculate in a similar manner for George and Mary, you will find that each one of them adds up to 57

Solution:

This statement is true but only in a specific case i.e. if both of the siblings continue to live till the day the younger is as old as the elder one was during the time of their birth.