Question 7.
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
A
41
B
42
C
40
D
43
Question Explanation
Text ExplanationVideo Explanation
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
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