If W is the set of all the integers between 10 and 332, 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 answers:
A) 111
B) 28
C) 160
D) 213
E) 107
Official Solution:   Number of multiples of 3   Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318   Step 2. Divide by 3: 318 / 3 = 106   Step 3. Add 1: 106 + 1 = 107.   So there are 107 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.   Number of multiples of 2   Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 330, the smallest is 12): 330 - 12 = 318   Step 2. Divide by 2: 318 / 2 = 159   Step 3. Add 1: 159 + 1 = 160.   So there are 160 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.   Add the 107 multiples of 3 and the 160 multiples of 2: 107+160=267.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take   107+160= 
<gadget id="calculator">  107+160</gadget>
<output>267</output>
267. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:   Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 330 - 12= 318   Step 2. Divide by 6: 318 / 6 = 53   Step 3. Add 1: 53 + 1 =54.   So there are 54 multiples of 6 within the range: we counted 54 numbers twice.   Subtract the 54 multiples of 6 from the sum of the multiples of 2 and 3:   = 107+160 - 54   = 267 - 54= 
<gadget id="calculator">267 - 54</gadget>
<output>213</output>
213   Therefore, the final number of multiples of 2, 3 or 6 is 213.   Hence, this is the correct answer. (213)
<result>D</result>
If W is the set of all the integers between 10 and 332, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?