If W is the set of all the integers between 69 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.
A) 20 B) 32 C) 33 D) 34 E) 35
Multiples of 2 from 69 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 68=[99/2]-[68/2]=49-34= 
<gadget id="calculator">49-34</gadget>
<output>15</output>
15   Multiples of 3 from 69 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 68=[99/3]-[68/3]=33-23= 
<gadget id="calculator">33-23</gadget>
<output>10</output>
10   Multiples of2 and 3 bothi.e.6 from 69 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 68=[99/6]-[68/6]=16-11= 
<gadget id="calculator">16-11</gadget>
<output>5</output>
5   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= 15 + 10 - 5= 
<gadget id="calculator">15 + 10 - 5</gadget>
<output>20</output>
20   20nswer Option 20
<result>A</result>
If W is the set of all the integers between 69 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?