If W is the set of all the integers between 29 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?  Choose the correct choice from the following options.
A) 26 B) 32 C) 33 D) 34 E) 47
Multiples of 2 from 29 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 28=[99/2]-[28/2]=49-14= 
<gadget id="calculator">49-14</gadget>
<output>35</output>
35   Multiples of 3 from 29 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 28=[99/3]-[28/3]=33-9= 
<gadget id="calculator">33-9</gadget>
<output>24</output>
24   Multiples of2 and 3 bothi.e.6 from 29 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 28=[99/6]-[28/6]=16-4= 
<gadget id="calculator">16-4</gadget>
<output>12</output>
12   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= 35 + 24 - 12= 
<gadget id="calculator">35 + 24 - 12</gadget>
<output>47</output>
47   Answer Option 47
<result>E</result>
If W is the set of all the integers between 29 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?