There are 3 sets of natural numbers 1 ot 100. Set A contains all the natural numbers which are prime, upto 100. Set B contains all the non-prime even natural numbers upto 100. Set C contains all the non-prime odd natural numbers upto 100 i.e.,
A = {2,3,5,7,11,...89, 97}
B = {4,6,8,10,12,...98,100}
C = {1,9,15,21,25,27,33,95,99}
The average of the Set C is :

Options

A. 52
B. 49.87
C. 55.46
D. can't be determined

Answer

To find the average of Set C, we will follow these steps:

### Step 1: Identify the elements of Set C
Set C contains all the non-prime odd natural numbers up to 100. The elements of Set C are:
C = {1, 9, 15, 21, 25, 27, 33, 35, 45, 49, 51, 55, 57, 63, 65, 69, 77, 81, 85, 87, 91, 93, 95, 99}

### Step 2: Count the number of elements in Set C
Now, we need to count how many elements are in Set C.
- The elements are: 1, 9, 15, 21, 25, 27, 33, 35, 45, 49, 51, 55, 57, 63, 65, 69, 77, 81, 85, 87, 91, 93, 95, 99
- There are 24 elements in total.

### Step 3: Calculate the sum of the elements in Set C
Next, we will sum all the elements in Set C:
Sum = 1 + 9 + 15 + 21 + 25 + 27 + 33 + 35 + 45 + 49 + 51 + 55 + 57 + 63 + 65 + 69 + 77 + 81 + 85 + 87 + 91 + 93 + 95 + 99

Calculating the sum:
- 1 + 9 = 10
- 10 + 15 = 25
- 25 + 21 = 46
- 46 + 25 = 71
- 71 + 27 = 98
- 98 + 33 = 131
- 131 + 35 = 166
- 166 + 45 = 211
- 211 + 49 = 260
- 260 + 51 = 311
- 311 + 55 = 366
- 366 + 57 = 423
- 423 + 63 = 486
- 486 + 65 = 551
- 551 + 69 = 620
- 620 + 77 = 697
- 697 + 81 = 778
- 778 + 85 = 863
- 863 + 87 = 950
- 950 + 91 = 1041
- 1041 + 93 = 1134
- 1134 + 95 = 1229
- 1229 + 99 = 1328

So, the sum of Set C is 1328.

### Step 4: Calculate the average of Set C
The average is calculated by dividing the sum by the number of elements:
Average = Sum of elements / Number of elements
Average = 1328 / 24

Calculating the average:
Average = 55.33 (approximately)

### Final Answer
The average of Set C is approximately 55.33.

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