Latest TCS Aptitude Question SOLUTION: If 12 divides ab313ab (in decimal notation, where a, b are digits > 0, the smallest value of a+b is

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If 12 divides ab313ab (in decimal notation, where a, b are digits > 0, the smallest value of a+b is

Asked In TCS prasanna (4 years ago)

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Read Solution (6) :

Ashokkumar  (4 years ago)

let us consider a=1,b=2
then 1231312 will not be divisible by 3 which is one of the factor of 12.
let us conider a=1,b=6
1631312 will be divisible by all factors of 12.hence a+b=1+6=7

Is this solution Helpfull? Yes (6) | No (1)  

Sandip yadav  (4 years ago)

4031340/12== 4+0=4

Is this solution Helpfull? Yes (4) | No (7)  

Subham Dash  (4 years ago)

ab313ab: To be divisible by 12 it must be divisible by 3 and 4.
Now the divisibilty rule of 4 says that the last two-digit number must be divisible by four.
ab=04,08 this cannot be true as (a and b>0)
ab=12(divisibility rule for four is satisfied but 3+1+3+2(a+b)=7+6=13 cannot be divisible by 3
ab=16(this can be divisible by both 3 and 4 so a=1,b=6 ,answer is a+b=7)

Is this solution Helpfull? Yes (3) | No   

kathirvel  (4 years ago)

3231332/12==0;3+2=5;

Is this solution Helpfull? Yes (2) | No (8)  

Devang Sharma  (4 years ago)

ab313ab is divisible by 12 ,means ab313ab is divisible by 3 and 4 .


condition 1 :- we know, any number is divisible by 3 when sum of all digits of number is divisible by 3.
so, a + b + 3 + 1 + 3 + a + b = 7 + 2(a + b)
therefore, 7 + 2(a +b) is integral multiple of 3.
e.g., 7 + 2(a+ b) = 3n
if n = 3 , (a + b) = 1
if n = 5 , (a + b) = 4
if n = 7, (a + b) = 7
hence, (a + b) = 1 + 3P , where P = {0, 1, 2, 3...}

condition 2:- now, one more condition is ab313ab is divisible by 4 , it is possible only when last two digit ab is divisible by 4


a , b > 0 , so we have to choose a and b in such a way that it a , b > 0 , (a + b) = 1+ 3P, where P is whole number and ab is divisible by 4.
we can choose a = 1 & b = 6 , a = 5 & b = 2, etc..
so, smallest value of (a + b) = 1 + 6 or (5+ 2) =7

hence, answer should be 7.

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ganesh babu  (4 years ago)

a, b >0
ab313ab/12
ab313ab/(3and4)
ab/4 possible 12,16,24,28,32,36,44,48,52,56,64,68,72,76,84,88,92,96
(a+b+3+1+3+a+b)=(2a+2b+7)/3
Possible a and b=16,28,52,64,76
a+b smallest value 7

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