Number of composite numbers lying between 67 and 101 is :

Options

A. 27
B. 24
C. 26
D. 23

Answer

To find the number of composite numbers lying between 67 and 101, we can follow these steps:

### Step 1: Identify the range
We need to find composite numbers between 67 and 101. This means we will consider the numbers from 68 to 100 (since 67 and 101 are not included).

### Step 2: Count the total numbers in the range
The numbers from 68 to 100 can be counted as follows:
- The first number is 68.
- The last number is 100.

To find the total count of numbers from 68 to 100, we can use the formula:
\[ \text{Total numbers} = \text{Last number} - \text{First number} + 1 \]
\[ \text{Total numbers} = 100 - 68 + 1 = 33 \]

### Step 3: Identify the prime numbers in the range
Next, we need to find the prime numbers between 68 and 100. The prime numbers in this range are:
- 71
- 73
- 79
- 83
- 89
- 97

Counting these, we find there are 6 prime numbers.

### Step 4: Calculate the number of composite numbers
Now, we can find the number of composite numbers by subtracting the number of prime numbers from the total count of numbers in the range:
\[ \text{Number of composite numbers} = \text{Total numbers} - \text{Prime numbers} \]
\[ \text{Number of composite numbers} = 33 - 6 = 27 \]

### Conclusion
Therefore, the number of composite numbers lying between 67 and 101 is **27**.

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