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integer qn

by purilisa » Sun Jul 18, 2010 7:52 pm
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

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by Rahul@gurome » Sun Jul 18, 2010 8:11 pm
In all there are 101 numbers between 200 and 300 inclusive
There are 51 numbers divisible by 2.
34 numbers divisible by 3 but 17 of them are also divisible by 2 so no need to count them again, hence numbers divisible by 3 = 17
21 numbers divisible by 5, but 11 numbers are also divisible by 2 and 3 numbers are divisible by 3, so numbers divisible by 5 = 7.
So, numbers not divisible by 2, 3, 5 = 101 - (51 + 17 + 7) = 26

The correct answer is [spoiler](E)[/spoiler].
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by rsnaren » Tue Jul 20, 2010 5:00 am
Is there any other shorter way for this?
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