If m+n gives remainder as 8 and m-n gives remainder as 6 when both are divide by 12, what is the remainder when m*n is divided by 6?

• let
  m+n=12a+8
  m-n=12b+6
  m*n=(6*(a+b)+7)(6*(a-b)+1))
  7%6=2
  ans = 1
• 11 years agoHelpfull: Yes(31) No(1)
• Let m=13,n=7
  hence
  m+n=20 and 20%12=8
  m-n=6 and 6%12= 6
  m*n= 91 and 91/6=1
• 11 years agoHelpfull: Yes(14) No(0)
• let no m = 7 n=1
  then both given condition satisfy this
  so 7/6 gives 1 as a remainder
  so , 1
• 11 years agoHelpfull: Yes(4) No(0)
• As there is confusion regarding the answer, i am giving an example of values for M and N
  
  Let M=19 and N= 13;
  Remainder when (M+N), that is (19+13) divided by 12 = 8
  Remainder when (M-N), that is (19-13) divided by 12 = 6
  Remainder when (M*N), that is (19*13)= 247 divided by 12 = 7
  
  So, 7 is the answer
• 11 years agoHelpfull: Yes(3) No(6)
• Lets assume the remainders when these numbers are divided by 12 be a and b respectively.
  
  The remainder when these two numbers are added, that is M+N is divided by 12 is nothing but the sum of a and b, so a+b is 8
  The remainder when M-N is divided by 12 will be either (a-b) 0r 12-(b-a), in the case, b>a
  If, a+b = 8 and a-b =6: a=7 and b=1
  If a+b=8, 12-(b-a)=6: here a=1 and b=7
  
  Example for the first case is numbers 31 and 13
  Example for the second case is 109 and 67
  
  But the question is not asking about the values of a and b, but only the product of a and b, that is the remainder when the product of M and N is divided by 12, that will be 7*1=7
  Answer is 7
• 11 years agoHelpfull: Yes(2) No(16)
• answer 1..............
• 11 years agoHelpfull: Yes(2) No(0)
• m+n=12k+8;
  m-n=12p+6;
  4*m*n=(m+n)^2-(m-n)^2
  ans is 7
• 11 years agoHelpfull: Yes(1) No(4)
• m+n/12=8;m+n=96
  m-n/12=6;m-n=72
  m=82;n=12
  m*n/6=82*12/6=164
  
• 11 years agoHelpfull: Yes(0) No(8)
• As it is 6 in the question, 1 is the answer.
  Sorry for the confusion
• 11 years agoHelpfull: Yes(0) No(0)
• answer is 7
• 11 years agoHelpfull: Yes(0) No(2)
• m+n=12x+8
  m-n=12y-6
  m=12(x+y)+14=6(2x+2y)+14
  n=12(x-y)+2=6(2x-2y)+2
  mn/6 produces a remainder of 4
  i.e (14*2)/6
  
• 11 years agoHelpfull: Yes(0) No(0)
• M=19
  N=1
  M*N=19%6=1
• 10 years agoHelpfull: Yes(0) No(0)