Made Easy Aptitude

Question

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

Comments

I think option c is right answer.

Answer 1

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

Comments

Why didn't you consider the middle term in the subset?

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cuzz it doesnot satisfies the solution protocol.

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care to elaborate?

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@Sambhrant Maurya,S is the subset of T which satisfies the condition as you can see S can have elements {(3,467) (11,459)(19,451)..........} as you can see total no. of elements are 59 and condition is satisfying in pair of equidistant from front and last .so there will be left one element in the middle which will not pair up with anyone.so only 29 pairs will be there which elements of subset S.

Answer 2

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

Comments

The answer is 29. I am in a dilemma too with this middle term.