Ratio between average of first four prime numbers and first four composite numbers is

Options

A. `13:10`
B. `17:27`
C. `11:27`
D. `17:19`

Answer

To find the ratio between the average of the first four prime numbers and the first four composite numbers, we will follow these steps:

### Step 1: Identify the first four prime numbers.
The first four prime numbers are:
- 2
- 3
- 5
- 7

### Step 2: Calculate the average of the first four prime numbers.
To find the average, we sum the prime numbers and divide by the count of the numbers.

Sum of the first four prime numbers:
\[ 2 + 3 + 5 + 7 = 17 \]

Average of the first four prime numbers:
\[ \text{Average} = \frac{\text{Sum}}{\text{Count}} = \frac{17}{4} = 4.25 \]

### Step 3: Identify the first four composite numbers.
The first four composite numbers are:
- 4
- 6
- 8
- 9

### Step 4: Calculate the average of the first four composite numbers.
Sum of the first four composite numbers:
\[ 4 + 6 + 8 + 9 = 27 \]

Average of the first four composite numbers:
\[ \text{Average} = \frac{\text{Sum}}{\text{Count}} = \frac{27}{4} = 6.75 \]

### Step 5: Calculate the ratio of the average of the first four prime numbers to the average of the first four composite numbers.
The ratio is given by:
\[ \text{Ratio} = \frac{\text{Average of Prime Numbers}}{\text{Average of Composite Numbers}} = \frac{4.25}{6.75} \]

### Step 6: Simplify the ratio.
To simplify \( \frac{4.25}{6.75} \), we can multiply both the numerator and the denominator by 100 to eliminate the decimal:
\[ \frac{425}{675} \]

Now, we can simplify this fraction. Both 425 and 675 can be divided by 25:
\[ \frac{425 \div 25}{675 \div 25} = \frac{17}{27} \]

### Final Answer:
The ratio between the average of the first four prime numbers and the first four composite numbers is \( \frac{17}{27} \).

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