If the median of `(x)/(2),(x)/(3),(x)/(4),(x)/(5),(x)/(6) ("where " x gt 0)` is 6 then x =

Options

A. 6
B. 18
C. 12
D. 24

Answer

To solve the problem, we need to find the value of \( x \) given that the median of the numbers \( \frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5}, \frac{x}{6} \) is 6.

### Step-by-Step Solution:

1. **Identify the Numbers**: We have the numbers:
\[ \frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5}, \frac{x}{6} \]

2. **Sort the Numbers**: Since \( x > 0 \), we can arrange these fractions in descending order:
\[ \frac{x}{2} > \frac{x}{3} > \frac{x}{4} > \frac{x}{5} > \frac{x}{6} \]

3. **Find the Median**: The median of a set of numbers is the middle value when the numbers are arranged in order. For 5 numbers, the median is the 3rd number:
\[ \text{Median} = \text{3rd score} = \frac{x}{4} \]

4. **Set the Median Equal to 6**: According to the problem, the median is given as 6:
\[ \frac{x}{4} = 6 \]

5. **Solve for \( x \)**: To find \( x \), multiply both sides of the equation by 4:
\[ x = 6 \times 4 \]
\[ x = 24 \]

### Final Answer:
Thus, the value of \( x \) is \( 24 \).

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