How many integers between 100 and 200, inclusive, cannot be evenly divided by 3 nor 5? Pick one: A) 46 B) 48 C) 50 D) 52 E) 54
The total numbers between 100 and 200, inclusive, is 101.   3*34= 
<gadget id="calculator">3*34</gadget>
<output>102</output>
102 and   3*66= 
<gadget id="calculator">  3*66</gadget>
<output>198</output>
198 so the number of multiples of 3 is 33.   5*20= 
<gadget id="calculator">5*20</gadget>
<output>100</output>
100 and   5*40= 
<gadget id="calculator">  5*40</gadget>
<output>200</output>
200 so the number of multiples of 5 is 21.   However, the multiples of 15 have been counted twice.   15*7= 
<gadget id="calculator">15*7</gadget>
<output>105</output>
105 and   15*13= 
<gadget id="calculator">  15*13</gadget>
<output>195</output>
195 so the number of multiples of 15 is 7.   Thus the total number is  101-33-21+7= 
<gadget id="calculator"> 101-33-21+7</gadget>
<output>54</output>
54.   The answer is 54.
<result>E</result>
How many integers between 100 and 200, inclusive, cannot be evenly divided by 3 nor 5?