If W is the set of all the integers between 49 and 88, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers? Choose one.
A) 11	B) 44	C) 48	D) 28	E) 26
Official Solution:   Number of multiples of 3   Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 87, the smallest is 51): 87 - 51 = 36   Step 2. Divide by 3: 36 / 3 = 12   Step 3. Add 1: 12 + 1 = 13.   So there are 13 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 88, the smallest is 50): 88 - 50 = 38   Step 2. Divide by 2: 38 / 2 = 19   Step 3. Add 1: 19 + 1 = 20.   So there are 19 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.   Add the 13 multiples of 3 and the 19 multiples of 2: 13+19=32.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   13+19= 
<gadget id="calculator">  13+19</gadget>
<output>32</output>
32. 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 32:   Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 84 - 54= 30   Step 2. Divide by 6: 30 / 6 = 5   Step 3. Add 1: 5 + 1 = 6.   So there are 6 multiples of 6 within the range: we counted 6 numbers twice.   Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:   =13+19 - 6   = 32 - 6= 
<gadget id="calculator">32 - 6</gadget>
<output>26</output>
26   Therefore, the final number of multiples of 2, 3 or 6 is 26.   Hence, this is the correct answer. (26)
<result>E</result>
If W is the set of all the integers between 49 and 88, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?