if r>x>0 and r+x=121, then what is the probability that 1/(1/r + 1/x) is a whole number . given that r and x both are whole number...

a) 1/10 b. 1/12 c. 1/11 d.) dont remember

• 1/12 is the answer...
  there would be 5 cases where it will give whole number....
  (66,55)...(77,44)..,(88,33)...(99,22)...(110,11)....
  out of the total no. of 60 case starting from (61,60) to (120,1)
  so 5/60 =1/12 the ans
• 9 years agoHelpfull: Yes(9) No(0)
• have u got right answer ?
  i think there is zero probability there is no any such chances that if x is less than r and 1/(1/r+1/x) is be whole number .
• 9 years agoHelpfull: Yes(1) No(0)
• i guess 1/12 is the correct answer .
  
  r+x=121 with r>x>0
  possible soln for this :
  r=120 x=1
  r=119, x=2
  ......
  ....
  ....
  r=61, x=60 i.e. 60 soln bcoz for r=60 x=61 r
• 9 years agoHelpfull: Yes(1) No(0)
• 1/60
  
  As 1/(1/r + 1/x)=r*x/(r+x) to be whole number r*x must be a multiple of (r+x)=121
  Checking the values for r*x= 121*n for n=1,2,.... we have 121, 242, 363, 484, 605, 726, 847, 968, 1089, 1210,....
  On observing these values 121=11*11, 242=11*22, 363=11*33,......,
  For one value to be 11 other must be 110 that satisfies condition , so r*x=1210=11*110 and
  For r+x=121, possible combinations of (r, x)=(1,120), (2,119), (3,118), ...........,(120,1), total 120
  Out of which (r,x)=(11, 110) and (110,11) i.e. 2 cases are favorable.
  So probability= 2/120=1/60
  
• 9 years agoHelpfull: Yes(1) No(5)
• @Devendra M ur approach is right but x must be less than r..
  @nikhil Gupta how is five possiblities ther??
• 9 years agoHelpfull: Yes(1) No(0)
• i didnt get ur solution plz elaborate...
• 9 years agoHelpfull: Yes(0) No(0)