If X = ( 163 + 173 + 183 + 193 ), then X divided by 70 leaves a remainder of


1) 0
2) 1
3) 69
4) 35

• X = 16^3+17^3+18^3+19^3
  X = (16^3+19^3)+(17^3+18^3)
  
  (x^n+y^n) is divisible by (x+y) for odd values of n
  
  (16^3+19^3) is divisible by 16+19=35
  (17^3+18^3) is divisible by 17+18=35
  
  so,X = (16^3+17^3+18^3+19^3) is divisible by 35
  
  also, X = ( 16^3 + 17^3 + 18^3 + 19^ 3 )is an even no. so, X is divisible by 2.
  [since, E+O+E+O=E]
  
  so, X is completely divisible by 35*2=70 & leaves a remainder 0
  
  1) 0
• 10 years agoHelpfull: Yes(70) No(2)
• here X = 16^3+17^3+18^3+19^3
• 10 years agoHelpfull: Yes(3) No(5)
• as we know that ->odd+odd=even
  and hence the sum of given number is even and thus->even/even=even
  and in the ans only 0 is even...
  Ans:0
• 9 years agoHelpfull: Yes(3) No(5)
• using formulae of first n^3
  f(n)=(n^2(n+1)^2 divided by 4)
  put n=19 u get 36100
  put n=15 u get 14400
  36100-14400=21700
  21700 divided by 70 gives remainder 0
• 9 years agoHelpfull: Yes(1) No(3)