Question

The numbers 2737 &1567 are divided by three digit number x, giving a same remainder.the sum of digit of x is

Answer 1

76. On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. What is the sum of the digits of N?A. 11B. 10C. 9D. 8

Here is the answer and explanation

Answer : Option B

Explanation :

Let 2272 ÷ N = a, remainder = r 

=> 2272 = Na + r ----------------------------(Equation 1)

Let 875 ÷ N = b, remainder = r 

=> 875 = Nb + r ----------------------------(Equation 1)

(Equation 1) - (Equation 2)

=> 2272 - 875 = [Na + r] - [Nb + r] = NA - Nb = N(a - b)

=> 1397 = N(a - b) ----------------------------(Equation 3)

It means 1397 is divisible by N

But 1397 = 11 × 127 

[Reference1 :how to find factors of a number?]

[Reference2 :Prime Factorization?]

You can see that 127 is the only 3 digit number which perfectly divides 1397 

=> N = 127

sum of the digits of N = 1 + 2 + 7 = 10