Latest TCS Aptitude Question SOLUTION: if ab133ab is divisible by 12. What is the minimum value of (a+b) ?

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

Asked In TCS Vinod Agarwal (11 years ago)

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ruby kumari  (11 years ago)

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.

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RAVINDRA KUMAR YADAV  (11 years ago)

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

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MIR FIROJ ALI  (11 years ago)

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).

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kishore   (11 years ago)

a=0 and b=4 ....
therefore a+b =4

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Rajat Dadhich  (11 years ago)

a=2 b=2 is also possible

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ANKIT SRIVASTAVA  (11 years ago)

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)

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m vinay kumar  (11 years ago)

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

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Aditya   (11 years ago)

@ Ravindra: why have u taken n=5 in 3*n, n should be 4 so as to be divisible by 12, right?

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ravikant  (11 years ago)

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

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m vinay kumar  (11 years ago)

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)

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rajapaul  (11 years ago)

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

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ashok  (9 years ago)

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..

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