a 2 digit number is 18 less than the square of the sum of the digits.how many such numbers are there?

1) 2
2) 3
3) 4
4) 5
5) 6

• Ans: Option 1
  Take N = 10a+b.
  Given that, 10a+b+18 = (a+b)2
  for a = 1 to 9, the L.H.S. will be, 28+b, 38+b, 48+b,.....,108+b.
  As LHS is perfect square for the values of b = 1 to 9, only  28+b, 48+b, 58+b, 78+b can be equal to 36, 49, 64, 81 for b = 8, 1, 6, 3 respectively.   But only 78+b = 81 for b = 3 So only one such number is possible. I.e, 63
• 9 years agoHelpfull: Yes(1) No(0)