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Let T be a set of integers {3,11,19,27,....451,459,467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum number of elements in S is?

a)32

b)28

c)29

d)30

2 Answers

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its the problem of A.P..

where a= 3, d=8 , and l=467.

using formulae a+(n-1)*d=l

n=59.

so floor(59/2) sum to 470.. (as sum of a term equidistant from ends are 470 except the middle one)

29 is answer . C

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I think the answer is D. 

Considering the middle term which is 235, it won't make the sum 470 with any other item in the set.

So 29 terms by solving the A.P. Series and one middle term also.

D) 30

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