If W is the set of all the integers between 39 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?  Choose one
A) 26 B) 32 C) 33 D) 34 E) 40
Multiples of 2 from 39 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 38=[99/2]-[38/2]=49-19= 
<gadget id="calculator">49-19</gadget>
<output>30</output>
30   Multiples of 3 from 39 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 38=[99/3]-[38/3]=33-13= 
<gadget id="calculator">33-13</gadget>
<output>20</output>
20   Multiples of2 and 3 bothi.e.6 from 39 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 38=[99/6]-[38/6]=16-6= 
<gadget id="calculator">16-6</gadget>
<output>10</output>
10   These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3   i.e. Total Numbers in W= 30 + 20 - 10= 
<gadget id="calculator">30 + 20 - 10</gadget>
<output>40</output>
40   Answer Option 40
<result>E</result>
If W is the set of all the integers between 39 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?