Question

There are 120 students waiting to go on field trip. The students are numbered 1 to 120, all even numbered students go on bus1, those divisible by 5 go on bus2 and those whose numbers are divisible by 7 go on bus3. How many students did not get in any bus?

Answer 1

`41` students did not get in any bus.

Explanation:

There are `120` students.

On `Bus1` even numbered i.e. every second student goes,

hence `120/2=60` students go.

Note that every tenth student i.e. in all `12` students, who could have gone on `Bus2` have left on `Bus1`.

As every fifth student goes in `Bus2`, number of students that go in bus (less `12` which have gone in `Bus1`) are `120/5-12=24-12=12`

Now those divisible by `7` go in `Bus3`, which is `17` (as `120/7=17 1/7`), but those with numbers `{14,28,35,42,56,70,84,98,105,112}` - in all `10` have already gone in `Bus1` or `Bus2`.

Hence in `Bus3` go `17-10=7`

Students left are `120-60-12-7=41`