If the median of \(x/5\), \(x/4\), \(x/2\), \(x\) and \(x/3\), where \(x\gt 0\), is 8, find the value of \(x\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 24
The median is the middle value once the data are arranged in order. Since \(x\gt0\), dividing by a larger number gives a smaller value, so from the smallest to the largest the values are \(\frac{x}{5},\frac{x}{4},\frac{x}{3},\frac{x}{2},x\).
There are five values, so the median is the 3rd one, \(\frac{x}{3}\)
\(\displaystyle\frac{x}{3}=8\), so \(x=24\)
Tip: The values are not printed in order. Taking the middle one as printed, \(\frac{x}{2}\), gives 16; always arrange the values first.