Solution:

11

Explanation:
We are looking at the numbers in the form of 5k +1 or 5k + 3
i.e The number ends in 1 or 3
If we jot down all such numbers, there are 16 in total:
1, 3, 11, 13, 21, 23, 31, 33, 41, 43, 51, 53, 61, 63, 71 and 73

Now, let us remove the ones that are not prime and we have the answer as:
3, 11, 13, 23, 31, 41, 43, 53, 61, 71 and 73

Solution:

Horse = 10
Cowboy-Boot = 1
HorseShoe= 2
The Last equation = 21

Detailed Explanation :
Equation1:
3Horse = 30
=> Horse = 10 .....(1)

Equation2:
1Horse + 2HorseShoe + 2HorseShoe = 18
10 + 4HorseShoe =18
HorseShoe = 2 .....(3)

Equation3:
2HorseShoe - 2Cowboy-Boot = 2
4 - 2Cowboy-Boot = 2
=> Cowboy-Boot = 1 ... (2)

Equation4:
Cowboy-Boot+Horse*HorseShoe = 1+10*2
=>21

Solution:

4%

Explanation:
The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

The solution is provided in the image below.

Solution:

9 - 8 + 76 - 5 + 4 + 3 + 21 = 100


Other ways of making number 100 (withiout using number 32)
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100
98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100
98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100
98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100
9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100

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:

930

Explanation:
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer

Solution:

Sam : 2
Dean : 5
Castiel : 7

Age diff
7 - 2 = '5' is prime
7 - 5 = '2' is prime
5 - 2 = '3' is prime

Solution:

522

Explanation:
1st Number = Number of alphabtes
2nd Number = Number of vowels
3rd Nummber = Number Of Circles

Lavesh = 6 alphabets + 2 vowels(a,e) + 2 circles(in 'a' and in 'e') = 622
Anmol = 5 alphabets + 2 vowels(a,0) + 2 circles(in 'a' and in 'e') = 522
Shruti = 6 alphabets + 2 vowels(u,i) + 0 circles = 620
Aakriti = 7 alphabets + 4 vowels(a,a,i,i) + 2 circles(in 'A' and in 'a') = 742
Hence,
Sonal = 5 alphabets + 2 vowels(a,o) + 2 circles(in 'a' and in 'o') = 522