How many integers between 100 and 190, inclusive, cannot be evenly divided by 3 nor 5? Choose the correct choice from the following answers
A) 42  B) 44  C) 46  D) 48  E) 50
The total numbers between 100 and 190, inclusive, is 91.   3*34= 
<gadget id="calculator">3*34</gadget>
<output>102</output>
102 and   3*63= 
<gadget id="calculator">  3*63</gadget>
<output>189</output>
189 so the number of multiples of 3 is 30.   5*20= 
<gadget id="calculator">5*20</gadget>
<output>100</output>
100 and   5*38= 
<gadget id="calculator">  5*38</gadget>
<output>190</output>
190 so the number of multiples of 5 is 19.   However, the multiples of 15 have been counted twice.   15*7= 
<gadget id="calculator">15*7</gadget>
<output>105</output>
105 and   15*12= 
<gadget id="calculator">  15*12</gadget>
<output>180</output>
180 so the number of multiples of 15 is 6.   Thus the total number is  91-30-19+6= 
<gadget id="calculator"> 91-30-19+6</gadget>
<output>48</output>
48.   The answer is 48.
<result>D</result>
How many integers between 100 and 190, inclusive, cannot be evenly divided by 3 nor 5?