Question

On dividing 2272 as well as 875 by a 3-digit number \[N\], we get the same remainder in each case. The sum of the digits of \[N\] is
A) 10
B) 11
C) 12
D) 13

Answer 1

Hint:
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. We will use this concept to find the value of that three digit number and then we will find the sum of the digits of that three digit number to get the required answer.

Complete step by step solution:
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.
\[ \Rightarrow {\rm{Difference}} = 2272 - 875 = 1397\] ……… \[\left( 1 \right)\]
1397 will be divisible by 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. \[N\] is 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.

Note:
Here we have obtained the factors of the number 1397 which was obtained by calculating the difference between the given numbers. Here factors of any number are defined as the numbers which divide the given number completely i.e. leaves zero remainder. In division, the number which is divided is known as dividend and the number which divides a given number is called divisor.