if ab133ab is divisible by 12. What is the minimum value of (a+b) ?

• a=4,b=0
  a+b=4
  a can't be 0 because most significant bit it is.n if a is 0 then it is not a 7 digit no.it "ll be 6 digit no.
• 12 years agoHelpfull: Yes(16) No(1)
• 12=4*3,so it must me divided by both 4 and 3.
  min condition of divisibility by 4 is 00 and 04.
  
  to be divided by 3, 2(a+b)+7=3*n. putting n=5, we get a+b=4
• 12 years agoHelpfull: Yes(9) No(1)
• add the digits, a+b+1+3+3+a+b=5+2*(a+b)
  to b divisible by 12
  the minimum value for (a+b)=7 (Ans).
• 12 years agoHelpfull: Yes(7) No(3)
• a=0 and b=4 ....
  therefore a+b =4
  
• 12 years agoHelpfull: Yes(3) No(1)
• a=2 b=2 is also possible
• 12 years agoHelpfull: Yes(1) No(9)
• by solving we get 2a+2b+7=3k--(1)(property of divisible by 3)
  and 3ab=4k(as we know divisible by4)---(2)
  by solving we get a+b=(3k-7)/2 it should be the integer value so k=3 (min value)
  by eqn 2--- ab=4 so its clear a=2 and b=2 hence a+b=4 (ans)
• 12 years agoHelpfull: Yes(1) No(1)
• sry i didn't see the qtn properly but in case of minimum the nos divisible by 4 starting from 1 to 99 are 4,8,12,16 the you should go for 4 i.e a=4,b=0
  a+b=4 ans.no is 4013340
• 12 years agoHelpfull: Yes(1) No(1)
• @ Ravindra: why have u taken n=5 in 3*n, n should be 4 so as to be divisible by 12, right?
• 12 years agoHelpfull: Yes(1) No(0)
• for divisibilty of 12,no must be divisble by 3,4...for 3 (2ab+7)divisble by3..
  means 2ab+1 divsible by 3and b such that it is divisble by 4 too so.a=5 b=8
  so a+b=13
• 12 years agoHelpfull: Yes(0) No(2)
• a,b are digits so (a+b+1+3+3+a+b).........(1) should be divisible by 3 and for divisibility by 4 (ab) should be divisible by 4....(2), it is given that a+b should be maximum so highest 2 digit nos divisible by 4 are 96,92,88,84 in these values only 88 satisfies the eqn so correct ans is 8+8 =16.(verify it if u have a calculator)
• 12 years agoHelpfull: Yes(0) No(2)
• ab133ab is divisible by 12
  so the last digits should be 2,4,6,8
  if it is 2 the expression is not divisible then 6 is divisible
  similarly a=1 ,b=6 the expresion becomes 1613316
  minimum value of a+b =7
• 12 years agoHelpfull: Yes(0) No(3)
• 4+0=4 is minimum in all a+b
  we can take 4013340 which is divisible by 12
  note::here there is no need of ab is minimum....there is a need of a+b is minimum..that's it...so answer is 4..
  
• 10 years agoHelpfull: Yes(0) No(0)