The range of x, 14, 17, 23, 26, and 46 is 33. Which of the following can be the value of x?

Options

A. 32
B. 74
C. 48
D. 26

Answer

To solve the problem, we need to find the value of \( x \) such that the range of the numbers \( x, 14, 17, 23, 26, \) and \( 46 \) is \( 33 \).

### Step-by-Step Solution:

1. **Understand the Range**:
The range of a set of numbers is calculated as the difference between the maximum and minimum values in the set.
\[ \text{Range} = \text{Maximum} - \text{Minimum} \]

2. **Identify Maximum and Minimum**:
In our case, the maximum value is \( 46 \) (since it is the largest number in the set) and the minimum value is \( x \) (since we are trying to find \( x \)).

3. **Set Up the Equation**:
According to the problem, the range is given as \( 33 \):
\[ 46 - x = 33 \]

4. **Solve for \( x \)**:
To find \( x \), we can rearrange the equation:
\[ 46 - 33 = x \]
\[ x = 46 - 33 \]
\[ x = 13 \]

5. **Conclusion**:
The value of \( x \) that satisfies the condition of the range being \( 33 \) is \( 13 \).