how many pairs of positive integers m,n satisfy
1/m + 4/n = 1/12

op: 3,4,5,6,7

• I think question is incomplete. There was condition given as n is odd integers less than 60.
  on solving above eq we get
  12n + 48m =mn
  mn - 12n - 48m = 0
  adding 576 both sides, we get
  mn - 12n - 48m + 576 =576
  (m-12)(n-48)=576
  since 576= 2^6*3^2
  so there are 7*3 = 21 factors.
  (so there are 21 natural no solutions of given ques without condition of n is odd integers less than 60. But there is not such option given hence ques is incomplete)
  now if n-48 is even then
  n=even+48 =even
  but we req to have n as odd ( missing condition in above ques)
  so n-48 = odd
  now
  (n-48) * (m-12)= 2^6*3^2
  (n-48) * (m-12)= 1*(2^6*3^2),,,, [n-48=1] so [n=49
• 9 years agoHelpfull: Yes(2) No(0)
• 1/m+4/n=1/12
  1/m=1/12-4/n
  n-48/12n
  m= 12n/n-48
  positive integral values of m for odd integral values of n are :
  n=37,49,51
  therefore 3 pairs are possible
• 9 years agoHelpfull: Yes(1) No(1)
• * n is odd integer and < 60
• 9 years agoHelpfull: Yes(0) No(0)
• so...576=2^6*3^2
  n-48 should be odd
  so..n-48 should be either 3^0 or 3^1 or 3^2.
  total 3 ways.
• 9 years agoHelpfull: Yes(0) No(0)