If m+n gives remainder 8 and m-n gives remainder 6 when divided by 12, then what is the remainder when mn is divided by 6?

• Answer is 1
  m+n=12x+8-------let x be divisor in this case
  m-n=12y+6-------let y be divisor in this case
  from the above two equations
  2m=12(x+y)+14
  2n=12(x-y)+2
  now multiplying the above two we get
  mn=12*3(x2-y2)+6(x+y)+42(x-y)+7
  On dividing the above equation with 6 we get "1" as remainder
• 9 years agoHelpfull: Yes(11) No(0)
• Assume that a is the remainder when m is divided by 12 and b is the remainder when n is divided by 12
  
  then a + b = 8 and a-b = 6
  
  or a = (8+6)/2 = 7 and b = 1
  
  When mn is divided by 6, the remainder will be the remainder of (7*1)/6 which is 1
• 9 years agoHelpfull: Yes(4) No(0)
• (m+n)/12 = 8
  => m+n = 96...........(i)
  & (m-n)/12 = 6
  => m-n = 72............(ii)
  from (i) and (ii) we get,
  m= 168 and n= 12
  now, (m*n)/6= 168*12/6
  = 168 ans.
• 9 years agoHelpfull: Yes(1) No(4)
• Dividend=divisor×quot+rem
  M+n=12×q+8
  M-n=12q+6
  0n solving these we have m=84&n=12
  So ans comes 168
• 9 years agoHelpfull: Yes(0) No(1)