How many integers between 100 and 160, inclusive, cannot be evenly divided by 3 nor 5?  Select the correct option.
A) 32  B) 27  C) 25  D) 35  E) 29
The total numbers between 100 and 160, inclusive, is 61.   3*34= 
<gadget id="calculator">3*34</gadget>
<output>102</output>
102 and   3*53= 
<gadget id="calculator">  3*53</gadget>
<output>159</output>
159 so the number of multiples of 3 is 20.   5*20= 
<gadget id="calculator">5*20</gadget>
<output>100</output>
100 and   5*32= 
<gadget id="calculator">  5*32</gadget>
<output>160</output>
160 so the number of multiples of 5 is 13.   However, the multiples of 15 have been counted twice.   15*7= 
<gadget id="calculator">15*7</gadget>
<output>105</output>
105 and   15*10= 
<gadget id="calculator">  15*10</gadget>
<output>150</output>
150 so the number of multiples of 15 is 4.   Thus the total number is  61-20-13+4= 
<gadget id="calculator"> 61-20-13+4</gadget>
<output>32</output>
32.   The answer is 32.
<result>A</result>
How many integers between 100 and 160, inclusive, cannot be evenly divided by 3 nor 5?