CAT 2020 Slot 3 QA Question & Solution
Number SystemsMedium
Question
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
Options
42
41
40
43
Solution
The number of multiples of 2 between 1 and 120 = 60
The number of multiples of 5 between 1 and 120 which are not multiples of 2 = 12
The number of multiples of 7 between 1 and 120 which are not multiples of 2 and 5 = 7
Hence, number of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7 = 120 - 60 - 12 - 7 = 41