The sum of four consecutive two digit odd numbers when divided by 10 become a prefect square. what are the consecutive numbers?

• ans : 37,39,41,43
  
  Let the numbers be (x-3),(x-1),(x+1),(x+3)
  
  their sum = (x-3)+(x-1)+(x+1)+(x+3)
  = 4x
  
  Given 4x/10 is a perfect square
  Also x is a 2 digit number
  
  ====> x = 40
  so the numbers are 37,39,41,43
• 10 years agoHelpfull: Yes(2) No(0)
• 37,39,41,43 wil be the numbers.
  (37+39+41+43)/10 = 160/10 = 16 = (4)^2
• 10 years agoHelpfull: Yes(1) No(1)
• Let the numbers be x-3,x-1,x+1,x+3.
  [(x-3)+(x-1)+(x+1)+(x+3)]/10=2x/5
  Since the digits are 2 digit integers this value(2x/5) can only be equal to 16 which gives x=40 and hence the numbers are 37,39,41,43.
• 10 years agoHelpfull: Yes(0) No(0)
• 7,9,11,13
  let the numbers be x,x+2,x+4 & x+6 . Where x is an odd number.
  now their sum will be 4x+12, and when divided by 10. They would be (2x+6)/5, this should be perfect square. For that by putting values of x at value 7 the desired resuld is attained. that is (2*7 +6)/5.It will be 4 and it is a perfect square. so the x is 7 and the four numbers are 7,9,11,13.
• 10 years agoHelpfull: Yes(0) No(0)
• answer is 7,9,11,13
  7+9+11+13=40
  40/10=4
  4 is a perfect square
  
• 10 years agoHelpfull: Yes(0) No(0)