If ab3133ab is divisible by 12.What is the minimum value of (a+b)?

• for ab3133ab/12 then it should be
  1. divisible by 4
  2. divisible by 3
  case 1.divisible by 4
  ab/4,
  take a and b 2 digits divisible by 4
  case2.put the values of a and b and then sum of the digits should be divisible by 3
  ex- take a=0,b=4
  perform the above steps
  hence ans is min(a+b)=4
• 12 years agoHelpfull: Yes(24) No(15)
• ab divisible by 12 means it should be div by 3&4
  so 1st we take 12, sub 12 instead of ab we get 12313312 it is not div by 3
  so try 16 gives 16313312 which is div by 3....
  so the ans is (1+6)=7
• 12 years agoHelpfull: Yes(16) No(17)
• for a number to b divisible by 12,it shd b divisible by 3 and 4
  for divisibility by 3 ---> a+b+3+1+3+3+a+b shd b divisible by 3
  for divisibility by 4 ---> ab shd b divisible by 4
  so when to consider from 00,01,02,... we get minimum ab is 40(it can be 04 too,but the 8 digit number given will be converted to 7 digit,which is not considerable.)
  so a+b=4.
  verification:
  for divisibility by 3,a+b+3+1+3+3+a+b shd b divisible by 3 => 2(a+b)+10 shd b divisible by 3. When we take a+b=4, 2(4)+10=18 wch is divisible by 3.
  
  SO,final answer is a+b=4.
• 12 years agoHelpfull: Yes(14) No(7)
• 1) this no shoud be divisible by both 3 and 4..
  so for 3 the sum of all the digit must be divisible by 3..it means
  a+b+3+1+3+3+a+b
  i.e. 2(a+b)+10 should be divisible by 3....the min no . is 18 when we put the value of a+b is 4......bcoz a+b is multiple of 2 so 15 can be formed....
  2) n for divisibilty of 4 the last 2 digit must be divisible by 4 it means ab=04 or 40.....
  so a+b=0+4=4
  or
  a+b=4+0=4
• 12 years agoHelpfull: Yes(5) No(6)
• correct question is where a,b >0.
  so correct answer is 7
  
• 9 years agoHelpfull: Yes(1) No(0)