Smithtown High School is holding a lottery to raise money. The tickets are assigned numbers from 1 to 200. Tickets with numbers divisible by 2 win t-shirts, tickets with numbers divisible by 3 win gift certificates, and tickets with numbers divisible by 7 win movie passes. How many tickets win none of the prizes?	Options:	A) 6	B) 52	C) 58	D) 142	E) 194
Total numbers divisible by:   3-&gt;200/3=66.66; Ignore the decimal part=66   2-&gt;200/2=100;   7-&gt;200/7=28.Something; Ignore decimal part=28   3*2-&gt;200/6=33   3*7-&gt;200/21=9   2*7-&gt;200/14=14   3*2*7-&gt;200/42=4   Thus, total numbers that can win prize= 66+100+28-33-9-14+4= 
<gadget id="calculator">66+100+28-33-9-14+4</gadget>
<output>142</output>
142 [:Note Used the same formula as we do for overlapping sets A∪B∪58=n(A)+n(B)+n(58)−n(A∩B)−n(A∩58)−n(B∩58)+n(A∩B∩58)   Non-winnable numbers=200-142= 
<gadget id="calculator">200-142</gadget>
<output>58</output>
58   Ans: "58"
<result>C</result>
Smithtown High School is holding a lottery to raise money. The tickets are assigned numbers from 1 to 200. Tickets with numbers divisible by 2 win t-shirts, tickets with numbers divisible by 3 win gift certificates, and tickets with numbers divisible by 7 win movie passes. How many tickets win none of the prizes?