NandishSS wrote:

How many even number in the range between 10 to 100 inclusive are not divisible by 3

A) 15

B) 30

C) 31

D) 33

E) 46

We can first determine the number of even numbers from 10 to 100 inclusive:

(100 - 10)/2 + 1 = 90/2 + 1 = 46

We know that if a number is even and it is also divisible by 3, then it’s divisible by 6. Therefore, we need to determine the number of multiples from 10 to 100 inclusive and exclude these multiples from the 46 even numbers we’ve determined.

The number of multiples of 6 from 10 to 100 inclusive is:

(96 - 12)/3 + 1 = 84/6 + 1 = 14 + 1 = 15

Since there are 46 even numbers and 15 multiples of 6 (which are divisible by 3) from 10 to 100 inclusive, there must be 46 - 15 = 31 even numbers that are not divisible by 3.

Answer: C

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