Question
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?
Answer: Option B
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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
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
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