Question:
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
Updated On: Sep 15, 2024
- 40
- 42
- 43
- 41
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The Correct Option is D
Approach Solution - 1
The required answer = \(120×\bigg(1-\frac{1}{2}\bigg)×\bigg(1-\frac{1}{5}\bigg)×\bigg(1-\frac{1}{7}\bigg) = 41.14\)
Required answer is the integral part of \(41.14 =41\)
So, the correct option is (D): \(41\)
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Approach Solution -2
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
So, number of the integers 1, 2,..., 120, which are divisible by none of 2, 5 and 7 = 120-60-12-7= 41
∴ Required Numbers are 41.
So, the correct option is (D): \(41\)
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