How many even number in the range between 10 to 100 inclusive are not divisible by 3  Choose the correct choice from the following options
A) 15
B) 30
C) 31
D) 33
E) 46
We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   10,12,14...100   using AP formula, we can say 100 = 10 + (n-1) *2   or n=46.   For 6,   12,18,...96   using AP formula, we can say 96 = 12 + (n-1) *6   or n=15.   Hence, only divisible by 2 but not 3 = 46-15= 
<gadget id="calculator">46-15</gadget>
<output>31</output>
31. hence, Answer 31
<result>C</result>
How many even number in the range between 10 to 100 inclusive are not divisible by 3