Aptitude - Numbers - Discussion

By divisibility rule of 11, we know that it's the difference between sum of number at odd places and sum of no. at even places must be zero or divisible by 11.

Hence we have,

7+3-(b+1), if we put 9 in place of b we get zero hence the condition is satisfied and the no. Is divisible by 11.

So the no. is 1397.

Now subtract 984 from 1397, we get 1397-984 = 413.

Hence a=1 and b=9.

And a+b = 10.

Just use the concept of divisibility of 11 and get the answer.

As number is 13b7 is divisible by 11 the difference of alternate digit must be zero or 11, so 1+b = 3+7 or (1+b) - (3+7) = 0. So you got b = 9.

A+8 = b, a+8 = 9 so a = 1, hence a+b = 10.

If b = 9 then,

4 a 3
9 8 4
-------
13 b 7

(4+9 = 13)(a+8 = 9)(3+4 = 7).

Let see, a+8 = 9.

> a = 9-8.

> a = 1.

Here a=1 is how declared please explain I can't understand?

Here they give two numbers 4a3 and 983.
And they said when they are added together, we get 13b7.
It means.

4 a 3.
9 8 4.
------
13 b 7.
--------

When we observe this.
If 3+4=7.
4+9=13 then a = 0 or 1.

We get b = 8 or 9.
And also they said that 13 b 7 is divisible by 11.

If we take b = 9 i.e.,
1397 it is divisible by 11.

So b = 9, a = 1.

Now a+b = 9+1 = 10.

If we add 4a3 to 984 then we can clearly see that the result is such a way that the digits in 100'ths place have no carry.

That means a+8 is always less than 9 in order to get 13b7 by comparing the places in addition the 10'ths digits underwent.

a+8=b --- (1).

Then 13b7 is divisible by 11 so the difference of sets, sum of even places and odd places in 13b7 is.

1+b-10=0 or multiple of 11.

Try 0.

Then b=9 which is less or equal to 9 hence by eq (1).

We can get answer.

If you try other than 11 then this adds up a carry in first addition of two number.

Guys i'm confused, how com we take a+8, is there simple method?

->211* 11=2321
now (2+2)-(3+1)=0.
simplify u got (9 - b)=0

How do we get (9 - b) = 0 Please explain.....

13b7 to know the divisibility of 11, we have to subtract sum of odd placed numbers with sum of even placed numbers.

in 13b7 odd places are 7and3

even places are b and 1.

now got it.