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

1) 250
2) 492
3) 493
4) 490

• 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(2)
• Thanks Dhanesh for the answer. But why haven't you considered 1 and 256 also ? Am I missing anything ?
• 7 years agoHelpfull: Yes(0) No(0)