How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?	Choose the correct choice.
A) 36  B) 38  C) 40  D) 42  E) 44
The total numbers between 100 and 170, inclusive, is 71.   3*34= 
<gadget id="calculator">3*34</gadget>
<output>102</output>
102 and   3*56= 
<gadget id="calculator">  3*56</gadget>
<output>168</output>
168 so the number of multiples of 3 is 23.   5*20= 
<gadget id="calculator">5*20</gadget>
<output>100</output>
100 and   5*34= 
<gadget id="calculator">  5*34</gadget>
<output>170</output>
170 so the number of multiples of 5 is 15.   However, the multiples of 15 have been counted twice.   15*7= 
<gadget id="calculator">15*7</gadget>
<output>105</output>
105 and   15*11= 
<gadget id="calculator">  15*11</gadget>
<output>165</output>
165 so the number of multiples of 15 is 5.   Thus the total number is  71-23-15+5= 
<gadget id="calculator"> 71-23-15+5</gadget>
<output>38</output>
38.   The answer is 38.
<result>B</result>
How many integers between 100 and 170, inclusive, cannot be evenly divided by 3 nor 5?