If the sum of two consecutive two digit odd numbers, divided by 7, it becomes a perfect square. Find the numbers ?

• (55,57) and (13,15)
• 11 years agoHelpfull: Yes(8) No(2)
• 55 and 57
  
  55+57 = 112
  112/7 = 16 = 4^2
• 11 years agoHelpfull: Yes(7) No(3)
• Purely Trail n Error:
  
  Consider Perfect squares first:
  1,4,9,16,25,36,etc
  
  Max sum of two consecutive two digit odd numbers: 99 n 97 =196
  
  Sum of two consecutive two digit odd numbers: So 1,4,9 cant be the answer . Also 36 * 7 =252 (Which exceeds 196) cant be the answer.
  
  16 or 25 must be the answer now.
  
  25 * 7 = 175(Sum of two odd number wont produce odd number again)
  
  So 16 must be answer (Again if u want 16 * 7= 112,,,, (112/2= 56) So consecutive two digit odd numbers are 55 n 57 .) :P
  
• 11 years agoHelpfull: Yes(4) No(7)
• The answer can also be 13 and 15
  The sum is 28, when divided by 7 it becomes 4 which
  is a perfect square of 2.
  Its not mentioned in the question that the perfect square
  is a double digit number. Only the two consecutive odd digits are
  given as double digits
• 11 years agoHelpfull: Yes(3) No(4)
• perfect multiples of 7.
  for ex:two odd nos 2n-1,2n+1.then add it wil be 4n.if n is perfect multiples of 7 like n=(1,4,9.....)*7
• 11 years agoHelpfull: Yes(1) No(2)
• 13,15
  2x+1+2x+3=4x+4
  hit n trail method
  
• 11 years agoHelpfull: Yes(1) No(0)