Solution:

19

Explanation:
77 empty bottles = 15 full bottles + 2 empty bottles
15 full bottles will give him 15 empty bottles more.
15 + 2 = 17
17 empty bottles = 3 full bottles + 2 empty bottles
3 full bottles will give him 2 empty bottles more.
3 + 2 = 5
5 empty bottles = 1 filled bottle

15 + 3 + 1 = 19

Thus we will be able to get 19 full bottles of soft drink.

Solution:

Box A has five balls and Box B has seven balls.

Solution:

2418

Explanation:
The rule that is being followed here is

P ~ Q ~ R ~ S = [first digit of (P * S)] [last digit of (Q * R)] [first digit of (Q * R)] [last digit of (P * S)]

Using the same rule in the incomplete equation,
7 ~ 2 ~ 7 ~ 4 = [first digit of (7 * 4)] [last digit of (2 * 7)] [first digit of (2 * 7)] [last digit of (7 * 4)]
= 2418

Thus 2418 is the missing number.

Solution:

The number is 281.

Solution:

18

Explanation:
Number of days with snow in morning and clear afternoon = A
Number of days with clear morning and snow in afternoon = B
Number of days with no snowfall in morning or afternoon = C

Now, number of days with snowfall = A + B = 13
Number of days with clear mornings = B + C = 11
Number of days with clear afternoons = A + C = 12

Adding these three equations, we get

2 * (A + B + C) = 36
Or, A + B + C = 18

Therefore, they spent eighteen days in total at their vacation.

Solution:

11550

Explanation:
There is just one way to find it out and that is the generic computing method.

The number of squares and rectangles formed = (Summation of column numbers)
= (1 + 2 + 3 +......+ 19 + 20) * (1 + 2 + 3 +......+ 9 + 10)
= 210 * 55
= 11550

Solution:

Assuming that John has A number of apples and Jacobs has B number of apples.

As per the question,
A + 1 = B - 1
=> B - A = 2 ------ (p)

Also, A - 1 = (B + 1) / 2
=> 2A - B = 3 ------ (q)

Solving (p) and (q)
A = 5 and B = 7

Therefore, A has 5 chocolates and B has 7 chocolates right now.

Solution:

The three numbers are:
-3, -1 and 1.

Solution:

Girl

Explanation:
In the House P:
There can be three possibilities.
Older Younger
Boy Girl
Girl Boy
Boy Boy
Since a boy is mentioned, we can't have a Girl-Girl option. Now all these options are equally possible and thus we will take them all into account. Two of the outcome have girls as an option and thus the probability here will be 2/3.

In the House Q:
We know that the elder child is a boy and thus there can be only two possibilities:
Older Younger
Boy Girl
Boy Boy

Here, the probability of having a girl child will be 1/2.

Thus you must choose the house P as we have better probability of having a girl in that house.

Solution:

18

Explanation:
Let us suppose that there were (3 * G) garlic bread sticks originally.

On dividing equally, the number of bread sticks with each of the friend = G

Each one of them ate four. The remaining sticks with each one of them = (G - 4)

Now, the total number of breadsticks left = 3 * (G - 4)
This number is equal to the breadsticks each one of them had after division.

=> 3 * (G - 4) = G
(3 * G) - 12 = G
2 * G = 12
G = 6.

Therefore, the number of breadsticks originally = 3 * G = 3 * 6 = 18.