Multiple choice

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 $N$?

  1. $8$
  2. $9$
  3. $10$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number N must divide the difference of the two numbers (2272 - 875 = 1397) to leave the same remainder. The factors of 1397 are 11 and 127. Since N is a 3-digit number, N = 127. The sum of the digits is 1 + 2 + 7 = 10.

AI explanation

Since the remainders are equal, the three-digit number N must perfectly divide the difference between 2272 and 875, which is 1397. The prime factorization of 1397 is 11 times 127, making the only three-digit number 127. The sum of its digits equals 1 plus 2 plus 7, which is 10.

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