Discussion
A student was supposed to multiply a positive real number \(p\) with another positive real number \(q\). Instead, the student divided \(p\) by \(q\). If the percentage error in the student's answer is 80%, the value of \(q\) is
Answer: D
The value of \(q\) is \(\sqrt{5}\).
The correct answer is \(pq\) and the student's answer is \(p/q\). The percentage error is
\[ \begin{aligned} \frac{pq - p/q}{pq} &= 1 - \frac{1}{q^{2}} = 0.8 \\ q^{2} &= 5,\quad q = \sqrt{5} \end{aligned} \]
Check the others: \(q = 5\) gives an error of 96%, \(q = 2\) gives 75%, and \(q = \sqrt{2}\) gives 50%.
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