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 female and excellent?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
The Excellent total comes from the fact that half of the students are either excellent or good; the male excellent students are then taken out of it.
Total students (32 females are 40% of all students):
\(\displaystyle \text{Total}=\frac{32}{0.40}=80\)
Excellent students (half of 80 are excellent or good, and 30 are good):
Excellent \(+\) Good \(=40\)
Excellent \(=40-30=10\)
Female excellent students (10 of the excellent students are male):
Female and excellent \(=10-10=\) 0