What was the number of schools having only facilities F1 and F3?

The correct answer is 42.

To understand why this is the correct answer, let us analyze the problem using the principles of set theory and Venn diagrams.

We are interested in finding the number of schools that have only facility F1 and facility F3. This means we are looking for schools that satisfy the following two conditions simultaneously:
1. They must possess both facility F1 and facility F3.
2. They must not possess facility F2.

In terms of set notation, if we denote the sets of schools having facilities F1, F2, and F3 as $F_1$, $F_2$, and $F_3$ respectively, the region representing schools with only F1 and F3 is given by the intersection:
$$F_1\cap F_3\backslash F_2$$
This can also be written as:
$$F_1\cap F_3\cap F_2^{\text{'}}$$
where $F_2^{\text{'}}$ represents the complement of set $F_2$ (schools without facility F2).

In a standard three-set Venn diagram, this region is the part of the intersection between the F1 circle and the F3 circle that lies strictly outside the boundary of the F2 circle. Based on the data, the value corresponding to this specific region is determined to be 42.