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The set S = {1,2,3,...,49,50}  contains the first 50 positive integers. After the multiples of 2 and the multiples of 3 are removed, how many integers remain in the set S?

 Aug 27, 2018
 #1
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+2

All multiples of 2 =50 / 2 = 25

All multiples of 3 that are odd =50/2 =16/2 =8

All multiples of 2  +  All multiples of 3 that are odd

25 + 8 =33. Therefore, the remaining numbers in the set are:

50 - 33 = 17 - Numbers remain in the set.

[1, 5, 7, 11,  13,  17, 19,  23, 25, 29, 31, 35, 37, 41, 43, 47, 49]

 Aug 28, 2018
 #2
avatar+98125 
+1

After the multiples of 2 are removed....there are 25  integers left

 

We are looking for the odd multiples of 3  [ the even ones have been accounted for ]  =   3 , 9 , 15, 21, 27, 33, 39, 45

 

Ther are 8  of these...so

 

25  - 8   = 17  integers   in set  S

 

 

 

cool cool cool

 Aug 28, 2018

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