Aptitude - Numbers - Discussion

@Payal.

It's 797.
When we add it to 5678 we get 35 as rem.
On dividing the sum by 460.

Let's make it simpler,

23*23 = 529.

To get a number closer to 1056.

529*2 = 1058.

What do we need to add to 1056 to make 1058?
1058-1056 = 2.

Whenever we divide any no then we want to break that no in such a group that each group contains equal no of elements.

For eg: If I divide 20/10 means I want to divide 20 in such groups that each group contains 10 elements here we get 2 is a no of groups that is our quotient. 20 is totally divided by 10 hence remainder is zero. In the above example (1056/23) also we have to break 1056 in groups of 23 elements. After division, it gives the remainder of 21 and quotient is 45. It is clear that if I add 2 more elements in a group of 21 then only I will get the 46th group of 23 elements and also get the no which is fully divided by 23.

So, 1056 + 2 = 1058 and 1058/23 gives quotient 46 and remainder as 0.

How can 1056-92 be 136?

It comes 964.

1056/23.

The simple method is;
The digit sum of 1056 = 12 = 3,
The digit sum of 23 = 5.

So what must be added to 3 to be divisible by 5 i.e 2 is the correct answer.

@ALL.

As per my method.

10 * 23 = 2300
2300/2 = 1150
1150-1056 = 94
94/23 = 4 quotient balance 2 ans is 2.

@Mohanagiri.

Smart approach, Thanks.

Basically we have to %(mod) operation here;

1056%23=
1056/23=45.91=46.
46*23=1058.
1058-1056=2 => answer.

When 1056 divided by 23 it yields 21 but we need to get "0" as remainder if we add +2 to 21 (i.e. 1058 it gives 23 as the remainder when it gets divided by 23) and it 23 get divided by 23 yields zero "0".

Simple,

They are asking only which is a least number make 1056 becomes divisible by 23.
So, we know divisibility means the remainder will be zero.

First, divide the1056 by 23.

And; we know 23*6=138, hence the given number 105(6) is must be 105(8) then we divided). Hence add 2 finally we get remainder zero.