N is a set of all natural numbers less than 500 which can be written as sum of two or more consecutive integers.Find the maximum number of elements possible in N?

1) 250
2) 491
3) 490
4) 499

• Answer - 492
  
  Any number, having atleast one odd number as a factor, can be written as the Sum of 2 or more Consecutive natural numbers.
  
  Eg. 9 = 2+3+4 or 4+5,
  17 = 8+9, 20 = 2+3+4+5+6
  
  Whereas, powers of 2 don't have any odd factor.
  
  There are 7 powers of 2, which are less than 500.
  2,4,8,16,32,64,128
  These cannot be written as the Sum of 2 or more Consecutive natural numbers.
  
  Hence, 499-7 = 492
• 8 years agoHelpfull: Yes(0) No(0)
• If we do not consider 0 as a natural number, then along with powers of 2, even 1 will be out of the scope.
  Eg. 1 = 0+1 cannot be valid
  
  Hence 499-7-1 = 491
  
  Answer - 491
• 8 years agoHelpfull: Yes(0) No(0)