If m+n is divided by 12 then the remainder is 8. And if m-n is divided by 12 then the remainder is 6. Find out the remainder when mn is divided by 6.

• m+n when divide by 12 leaves rem 8=> 12x+8=m+n
  m-n when divided by 12 leaves rem 6=> 12y+6=m-n
  Solving both we get m=6(x-y)+1 and n=6(x+y)+7
  mn will give u (6(6(x+y)(x-y))+7)/6 .So 36*(any thing ) would leav 0 rem,7 when divide would leav 1 as rem
• 11 years agoHelpfull: Yes(29) No(1)
• Let M+N=20 (Bcoz So As To Leave Remainder as 8 When Divided By 12)
  
  Let M-N=18 (So As To Leave The Remainder As 6 When Divided By 12)
  
  By Solving Above 2 Equations We Get M=19 & N=1
  
  Then M*N= 19 When Divided by 6 Gives Remainder as 1
  
  So Ans Is Remainder Equal To 1
• 8 years agoHelpfull: Yes(19) No(1)
• REMAINDER IS 1....@SRAVYA PLZZ RECHECK UR ANSWER...ND 25*7=175 NOT 105 MIND IT...:)
• 11 years agoHelpfull: Yes(10) No(2)
• let us assume m+n=20
  and m-n=18
  now,find m and n
  then m×n
  check it by dividing 6
  and then the solution.
  
  the answer will be 1.
  By assuming things you can get rid of long equations :)
• 9 years agoHelpfull: Yes(8) No(1)
• from the given data m=25,n=7
  m+n=32,32/12=8(remainder)
  m-n=18,18/12=6(remainder)
  m*n=105,105/6=3(remainder)
  hence 3 is the ans..
• 11 years agoHelpfull: Yes(4) No(10)
• m+n=12x+8
  m-n=12y+6
  (m+n)/12= 0 rem + (8/12)
  then (m+n)=8
  so num. can be replaced by its remainder
  similarly
  (m-n)=6 solving equ , m=7 & n=1
  therefore 7/6 rem is 1.
• 9 years agoHelpfull: Yes(4) No(0)
• ya sorry 25*7=175
  so remainder for 175/6=1
• 11 years agoHelpfull: Yes(2) No(1)
• sry rem is not 7
  1 is correct answer
  
• 11 years agoHelpfull: Yes(2) No(1)
• hi Sravya,how we will find 25 and 7 value during the short time of exam
• 11 years agoHelpfull: Yes(1) No(2)
• 
  m + n = 12a + 8 ⇒ (m+n)2=144a2+192a+64 - - - (1)(squaring both sides)
  m - n = 12b + 6 ⇒ (m−n)2=144b2+144b+36 - - - (2)
  (1) - (2) ⇒ 4mn = 144a2+192a−144b2−144b+28
  mn = 36a2+48a−36b2−36b+7
  Now mn is divided by 6, all the terms except 7 gives 0. So 7 divided by 6, remainder = 1
  
• 9 years agoHelpfull: Yes(1) No(0)
• remainder is 7
• 11 years agoHelpfull: Yes(0) No(6)
• 1 wil be the remaindrr
• 11 years agoHelpfull: Yes(0) No(0)
• would leav 1 as rem
• 11 years agoHelpfull: Yes(0) No(0)
• let m+n=32------eqn(1)
  m-n=30-------eqn(2)
  solving both eqn 1 & 2 we get
  m=31 and n=1 then mn=31
  and from Q mn/6
  (31*1)/6=1
  hence Remainder will be 1 ans
• 9 years agoHelpfull: Yes(0) No(0)
• m+n-8 when divide by 12 gives remainder 0 => m+n-8/12=0 =>m+n-8=0
  m-n-6 when divide by 12 gives remainder 0 =>m-n-6/12=0 => m-n-6=0
  solving m+n-8=0 and m-n-6=0 we will get m=7,n=1
  mn/6 =>7/6 gives remainder 1
• 8 years agoHelpfull: Yes(0) No(1)
• m + n = 12a + 8 ⇒ (m+n)2=144a2+192a+64
  (m+n)2=144a2+192a+64
  - - - (1)
  m - n = 12b + 6 ⇒ (m−n)2=144b2+144b+36
  (m−n)2=144b2+144b+36
  - - - (2)
  (1) - (2) ⇒ 4mn = 144a2+192a−144b2−144b+28
  144a2+192a−144b2−144b+28
  
  mn = 36a2+48a−36b2−36b+7
  36a2+48a−36b2−36b+7
  
  Now mn is divided by 6, all the terms except 7 gives 0. So 7 divided by 6, remainder = 1
  
  
• 8 years agoHelpfull: Yes(0) No(0)
• wwould leave 1 as remainder
• 6 years agoHelpfull: Yes(0) No(0)
• Let to get remainder 8
  M+N=20
  Also to get remainder 6
  M-N=18
  By solving the equation we get m=19
  N=1
  So using m and n value we get remainder 1 if the M*Nnumber is divided by 6
• 6 years agoHelpfull: Yes(0) No(0)