Aptitude - Numbers - Discussion

4 a 3
+9 8 4
----------
1 3 b 7
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If any any number added to 8 which is greater than 2 or equals to 2 gives a carry so choose the number in place of a which is less than 2.

8+a = 8+1 = 9 which doesn't give a carry so a=1.

4 1 3
+9 8 4
---------
1 3 9 7 -----> which is divisible by 11.
-----------
a=1, b=9.
a+b=1+9=10.

How can you got (9 - b) I cannot understand. Please, Explain

Nice explanation dudes.

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.

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.....