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
Shwetank Mauria
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#

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