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?

1 Answer
May 14, 2016

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