Solution:

Let us denote the number of boys as 'p' and the number of girls as 'q'.

The first statement says that each boy has equal numbers of brothers and sisters
(p - 1) = q
=> p - q = 1 ------- (a)

The second statement says that every girl has twice as many brothers as that of sisters
2 (q - 1) = p
=> 2q - p = 2 ------- (b)

By solving (a) and (b)
We get q as 3 and p as 4.

Therefore, there are 4 boys and 3 girls in the family.

Solution:

7 Races.

Solution:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

Solution:

63.984375

Explanation:
This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:

Year Amount Interest and Deduction
Start 63.984375
Y1 End 62.968750 63.984375 * 2 - 65
Y2 End 60.937500 62.96875* 2 - 65
Y3 End 56.875000 60.9375 * 2 - 65
Y4 End 48.750000 56.875 * 2 - 65
Y5 End 32.500000 48.75 * 2 - 65
Y6 End 0.000000 32.5 * 2 - 65 = 0

Solution:

As you see in the image, we had to move just the circle number 1, 7 and 10 and it is done.

Solution:

Flyball should pay Lavy $11 instead of accepting his counter offer as in that case the club will end up paying almost double the amount.

Solution:

3

Explanation:
Possible matches
Chelsea vs Tottenham
Chelsea vs ManCity
Chelsea vs Arsenal
Chelsea vs Liverpool
Tottenham vs ManCity
Tottenham vs Arsenal
Tottenham vs Liverpool
ManCity vs Arsenal
ManCity vs Liverpool
Arsenal vs Liverpool

Therefore there is a total of 10 matches. After every match, 2 points were distributed between two teams as:
Case1: One of team wins:
Winning team will get 2 points.

Case2: Match ends up in a draw
Both teams will share a point.

Therefore 10*2 = 20 points should be the sum of all team points.

6 + 5 + 4 + 2 + ? =20
? = 3

Solution:

==== 65 ==== 35 ====
== 34 === 31 === 4 ==
= 10 == 24 == 7 == -3 =

Solution:

$2000

Explanation:
Profit from 1st transaction = $1000 (23000-22000)
Profit from 2nd transaction = $1000 (24000-24000)

So the overall profit will be = $2000.