A teacher keeps data on students tabulated by performance and gender of the students. The data is on a computer disc but unfortunately some of it is lost due to a technical glitch. Only the following data could be recovered:
| Gender | Performance | Total | ||
| Average | Good | Excellent | ||
| Male | - | - | 10 | - |
| Female | - | - | - | 32 |
| Total | - | 30 | - | - |
An expert committee was formed which decided that the following facts were self-evident: half of the students were either excellent or good; 40% of the students were female; one-third of the male students were average.
How many students are both male and good?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 22
The male students are split into Average, Good and Excellent, so the male good students are what is left after the average and the excellent males are taken out.
Total and male students (32 females are 40% of all students):
\(\displaystyle \text{Total}=\frac{32}{0.40}=80\)
Male \(=80-32=48\)
Male good students (one-third of the males are average; 10 males are excellent):
Male average \(\displaystyle =\frac{48}{3}=16\)
Male and good \(=48-16-10=\) 22