Question 14
A sample of university staff and students was asked whether they preferred catching public transport or driving their own car to university. The data collected is shown in the table.
| Public transport | Drive own car | |
|---|---|---|
| Staff | 2 | 18 |
| Students | 48 | 12 |
What percentage of university students prefer to drive their own car?
Not quite. 12 is the raw count from the table, the number of students who prefer to drive, written as if it were already a percentage. A count only becomes a percentage once you divide it by the right total.
Not quite. 15% is $\frac{12}{80}\times100\%$, which divides by all 80 people surveyed, staff included. The question only asks about students, so the 20 staff don’t belong in the whole.
That’s it. Step through the hints below to see why.
Not quite. 40% is $\frac{12}{30}\times100\%$, which divides by the 30 people who prefer to drive. That answers a different question: what percentage of the drivers are students?
| Public transport | Drive own car | Total | |
|---|---|---|---|
| Staff | |||
| Students | |||
| Total |
The part is always the 12 students who prefer to drive. What changes the answer is which whole you divide by.
This is option (A). Writing the count 12 with a % sign doesn’t make it a percentage. It would only be right if exactly 100 students were surveyed, and here there are 60.
This is option (B). It answers “what percentage of everyone surveyed are students who prefer to drive?” The 20 staff are in the whole, and the question didn’t ask about them.
This is option (C). It answers the question that was asked: of the university students, what percentage prefer to drive?
This is option (D). It answers “what percentage of the people who prefer to drive are students?” The 18 staff drivers are in the whole, so it’s the wrong group.
Read the question for the group. “What percentage of university students prefer to drive their own car?” The words after “of” name the whole.
The whole is the Students row. Staff aren’t part of this calculation at all.
The table doesn’t show totals, so add the row yourself.
$$\text{Students: }48+12=60$$
This is a row percentage, because the group the question names is a row. The 80 (everyone) and the 30 (all drivers) are totals for other questions.
$$\frac{12}{60}\times100=20\%$$
Check the size. 12 is one-fifth of 60, and one-fifth is 20%.
The QCAA used this question in its 2020 subject report to show how each wrong option was built: 12 written straight down as 12%, then 12 over 80, then 12 over 30. Every wrong option is built from real numbers in this table.
$$\begin{aligned}\text{students}&=48+12=60\\\frac{12}{60}\times100&=20\%\end{aligned}$$
The group named in the question is the students, so divide by the Students row total. The 2020 subject report lists the slips behind the other options: (A) the raw count 12 stated as a percentage, (B) $\frac{12}{80}\times100\%$ and (D) $\frac{12}{30}\times100\%$.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording is from the 2020 QCAA General Mathematics external assessment, © State of Queensland (QCAA) 2020, licensed under CC BY 4.0, and has been adapted. Tangent Tuition is not affiliated with the QCAA.
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