How many even number in the range between 10 to 140 inclusive are not divisible by 3
Choose the correct choice from the following
A) 15 B) 30 C) 31 D) 33 E) 44
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...140   using AP formula, we can say 140 = 10 + (n-1) *2   or n=66.   For 6,   12,18,...138   using AP formula, we can say 138 = 12 + (n-1) *6   or n=22.   Hence, only divisible by 2 but not 3 = 66-22= 
<gadget id="calculator">66-22</gadget>
<output>44</output>
44. hence, Answer 44
<result>E</result>
How many even number in the range between 10 to 140 inclusive are not divisible by 3