manalq8 wrote:

What is the number of integers from 1 to 1000 (inclusive) that are divisible by neither 11 nor by 35?

884

890

892

910

945

what's the quickest way to solve this questions do you think?

I will provide the my approach and the OA once I see yours

thanks alot

Normally, I would use the method used by Bunuel. It's the most accurate. But if you are looking for a speedy solution, you can use another method which will sometimes give you an estimate. Looking at the options (most of them are spread out), I wont mind trying it. (Mind you, the method is accurate here since the numbers start from 1.)

In 1000 consecutive numbers, number of multiples of 11 = 1000/11 = 90 (Ignore decimals)

In 1000 consecutive numbers, number of multiples of 35 = 1000/35 = 28

Number of multiples of 11*35 i.e. 385 = 1000/385 = 2

Number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - (90 + 28 - 2) {Using the concept of sets here) = 884

Think: Why did I say the method is approximate in some cases?

Think what happens if the given range is 11 to 1010 both inclusive (again 1000 numbers)

What is the number of multiples in this case?

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