A number is greater than 3 but less than 8. Also, it is greater than 6 but less than 10. The number is

Options

A. 5
B. 6
C. 7
D. 8

Answer

To solve the problem step by step, let's break down the conditions given in the question.

### Step 1: Understand the conditions
We need to find a number \( X \) that satisfies the following conditions:
1. \( 3 < X < 8 \)
2. \( 6 < X < 10 \)

### Step 2: Analyze the first condition
From the first condition \( 3 < X < 8 \), we can determine that the possible values for \( X \) must be greater than 3 and less than 8. This means \( X \) can be any number in the range (3, 8).

### Step 3: Analyze the second condition
From the second condition \( 6 < X < 10 \), we can determine that the possible values for \( X \) must be greater than 6 and less than 10. This means \( X \) can be any number in the range (6, 10).

### Step 4: Find the intersection of the two conditions
Now, we need to find the values of \( X \) that satisfy both conditions simultaneously.

- The first condition gives us the range (3, 8).
- The second condition gives us the range (6, 10).

The overlapping range (intersection) of these two conditions is:
- \( 6 < X < 8 \)

### Step 5: Identify possible integer values
Now, we need to find integer values that lie within the range \( 6 < X < 8 \). The only integer that satisfies this condition is:
- \( X = 7 \)

### Conclusion
Thus, the number that satisfies both conditions is:
- **7**