Question

If the median of \( \frac{x}{5}, x, \frac{x}{4}, \frac{x}{2} \) and \( \frac{x}{3} \) (where \(x > 0\)) is 8, then the value of \(x\) will be

• A. \( 24 \)
• B. \( 32 \)
• C. \( 8 \)
• D. \( 16 \)

Hint:

\textbf{Median of a Data Set.} To find the median of a data set, first arrange the data in ascending or descending order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.

Answer 1

The Correct Option is A

First, we need to arrange the given values in ascending order. Since \(x > 0\), we can compare the fractions by comparing their denominators: 2, 3, 4, 5. The order of the fractions will be inversely proportional to the denominators. So, the order is: $$ \frac{x}{5} < \frac{x}{4} < \frac{x}{3} < \frac{x}{2} < x $$ The given set of values in ascending order is: $$ \frac{x}{5}, \frac{x}{4}, \frac{x}{3}, \frac{x}{2}, x $$ There are 5 values in the set, which is an odd number. The median of a set with an odd number of values is the middle value when the values are arranged in ascending order. In this case, the middle value is the \(\left(\frac{5+1}{2}\right)^{th} = 3^{rd}\) value, which is \( \frac{x}{3} \). We are given that the median of the set is 8. Therefore, $$ \frac{x}{3} = 8 $$ Multiplying both sides by 3, we get: $$ x = 8 \times 3 $$ $$ x = 24 $$ So, the value of \(x\) is 2(D)