For any real number x , let [x] denotes the integer part of x ; x be the fractional part of x ( x =x-|x|) . Let A denote the set of all real numbers x satisfying x = x+[x]+[x+(1 / 2)] 20 If S is the sum of all numbers in A , find [S]

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Quantrex Academy · Accepted Answer

Correct answer: 21

Let, x=l+f given equation reduces to, f= I+f+I+I+ [f+ 1 2 ] 20 array ll (l) & f [0, 1 2 ) & [f+ 1 2 ]=0 & 19 f=3 l f= 3 l 19 & 0, < 3 l 19 < 1 2 & l [0, 19 6 ) l=0,1,2,3 & f=0, 3 19 , 6 19 , 9 19 & x=0, 22 19 , 44 19 , 66 19 array array ll (II) & f [ 1 2 , 1 ] & [f+ 1 2 ]=1 & 20 f=3 l+1+f & f= 3 l+1 19 & 1 2 3 l+1 19 < 1 17 6 l < 6 l=3,4,5 & f= 10 19 , 13 19 , 16 19 & x= 67 19 , 89 19 , 111 19 & S= 399 19 & [S]=21 array

For any real number x , let [x] denotes the integer part of x ; x be the fractional part of x ( x =x-|x|) . Let A denote the set of all real numbers x satisfying x = x+[x]+[x+(1 / 2)] 20 If S is the sum of all numbers in A , find [S]

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