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Re: set theory
by rahul srivastav - Sunday, 16 September 2012, 03:22 PM
  mow i understood perfectly..thanks a lotsmile

can u hlp me solve these 2 prblms frm no. system

1)A = {3, 23, 43 ………… 603} and S is a subset of A. If the sum of no two elements of S is more than 606, then what can be the maximum possible number of elements in S?

ans.16

2)The HCF of three natural numbers x, y and z is 13. If the sum of x, y and z is 117, then how many ordered triplets (x, y, z) exist?

ans.27(here i did up to x+y+z=9,after this i am unable to proceed.)
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Re: set theory
by vivek 231 - Sunday, 16 September 2012, 04:12 PM
  hi rahul,

the no of terms in the set is 31 it can be obtained by the formulae 3+(n-1)20=603 it has 31 elemetns in the subset


for the new subset to be formed the sum of any two terms should not be more than 606 if u take the mid term of the set given it is
303 if u add the 303 with any of the numbers till 15th term of the series u will not get the sum more than 606,

but if u take the 17th term of the series u will get the sum of 303 and 323 as 626 now it violates the given condition so the no of terms is 16

hope it's right and you are clear about the conceptsmile
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Re: set theory
by rahul srivastav - Sunday, 16 September 2012, 04:20 PM
  it's clear but how did u knew it is the middle term??
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Re: set theory
by vivek 231 - Sunday, 16 September 2012, 06:03 PM
  hi rahul

for the first 31 terms of an a.p the 16th term is the middle one
it will have 15 terms after it and 15 terms before it
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