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
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 24
The median is the middle value once the values are put in order. As \(x\gt0\), a fraction of \(x\) is smaller when its denominator is larger, so the order is easy to write down.
In increasing order: \(\displaystyle\frac{x}{5},\ \frac{x}{4},\ \frac{x}{3},\ \frac{x}{2},\ x\)
There are 5 values, so the median is the 3rd: \(\displaystyle\frac{x}{3}\)
\(\displaystyle\frac{x}{3}=8\), so \(x=24\)