Aptitude - Numbers - Discussion

Where did 11 and 127 comes from?

Please explain.

Here we need to find the sum of the digits of the required 3-digit number.
As the given two numbers when divided by 3-digit numbers give the same remainder then that means when we find the difference between them then that difference will be divisible by that three-digit number.

So, we will first find the difference between the given numbers, i.e. 2272 and 875.

Difference=2272-875=1397 --->(1)

1397 will be divisible by a three-digit number i.e. N.
.
We know that the factors of the number 1397 are 11 and 127.
The only three-digit number which has a factor of 1397 is 127.
So, we can say that the value of the three-digit number i.e. N.
It's equal to 127.
Now, we will find the sum of the digits of the N.
The sum of the digits of N.
=1+2+7=10.
Hence, the correct option is option A.

@All.

Here is the solution.

2272-R=0(mod N).
875-R=0(mod N).
2272-875=0(mod N).
1397=0(mod N).

So, any factor of 1397 can be the answer for N which 127 will be correct according to the question given (3digit numbers).

1+2+7=10.

2272 - 875 = 1397 which is divisible by 11.
i.e. , 1397 = 11 X 127.
so, 1+2+7 = 10.