In S you can see 4*3=12 so the set becomes 4,8,12,16,20,24,28,32,36,40,...... .Now you can see the 3rd , 6th , 9th , .... element are multiples of 12 ,so the multiples of 12 in S are in 3p ( values of p will determine the position of multiples of 12 in set S) positions. Now here comes the interesting part of the problem. Think carefully what we can do with this information and hint!!!!!!
[/et_pb_tab][et_pb_tab title="Hint 5" _builder_version="4.0"]Step 5 .So now you know that every 3rd element in S will be a multiple of 12 .So you have to calculate [\(\frac{2005}{3}\)] where [.] is the greatest integer function (Which means as many time this 3rd position or the 3p form appears in the set you will get a multiple of 12 so we will use the greatest integer function in order to find out the multiples of 12 in S).Therefore [\(\frac{2005}{3}\)]=668. which is your required answer
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