CAT 2020 Exam Shift 3 Solved Paper

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.
F1: Own software for OTLP
F2: Trained teachers for OTLP
F3: Training materials for OTLP
F4: All students having Laptops
The following observations were summarized from the survey.
1. 80 schools did not have any of the four facilities $-\mathit{F}1,\mathit{F}2,\mathit{F}3,\mathit{F}4$.
2. 40 schools had all four facilities.
3. The number of schools with only $\mathit{F}1$, only $\mathit{F}2$, only $\mathit{F}3$, and only F4 was $25,30,26$ and 20 respectively.
4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
5. 313 schools had F2.
6. 26 schools had only $\mathit{F}2$ and $\mathit{F}3$ (but neither $\mathit{F}1$ nor $\mathit{F}4)$.
7. Among the schools having $\mathit{F}4,24$ had only $\mathit{F}3$, and 45 had only $\mathit{F}2$.
8. 162 schools had both $\mathit{F}1$ and $\mathit{F}2$.
9. The number of schools having F1 was the same as the number of schools having F4.