no. of integers divisible

[cypherskull]

How many positive integers between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?

A. 3

B. 16

C. 75

D. 24

E. 26

[aneesh.kg]

There are 101 integers from 200 to 300.
The 51 integers that are even will be divisible by 2. Exclude them.
50 remaining.
How many odd multiples of 3 are there?
Starting from 201 to 297, there are 17 such integers. (Use AP formula: last term = a
+ (n - 1)*d to count). Exclude them.
33 remaining.
How many multiples of 5 are neither divisible for 2 nor 3. 205, 215, 235, 245, 265, 275, 295.
7 such numbers. Exclude them too.
26 remaining.

[spoiler](E)[/spoiler] is the answer.

[satyavegi]

Can you please explain the concept on how to tackle this kind of questions ..

general mistakes we do here are counting twice or sometimes taking as 100 numbers as in between instead of 101.

can you brief this area

thanks

[aneesh.kg]

Oh yes.

Read this:
https://www.beatthegmat.com/finding-the- ... tml#470942

This will you help you reduce your mistakes in counting.
In this question, however, you've to be a little careful about which numbers have already been considered. for e.g. when the multiples of 5 had to be counted, one had to be really careful to rule out the multiples of 2 (210, 220,..) and multiples of 3 (such as 225, 255, 285) because they had already been counted.

[amit28it]

The answer calculated by aneesh.kg is absolutely correct not only the answer but the method used is also the simplest one and my answer is exactly the same that is E.
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