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The numbers 2272 and 875 are divided by a 3-digit number N, giving the same remainders. The sum of the digits of N is
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- 10
- 11
- 12
- 13
Correct Option: A
Let the remainder in each case be x.
Then, (2272 – x) and (875 – x) are exactly divisible by that three digit number.
Hence, their difference [(2272 – x) – (875 – x)] = 1397 will also be exactly divisible by the said divisor (N).
Now, 1397 = 11×127 Since both 11 and 127 are prime numbers, N is 127.
∴ Sum of digits = 1+ 2 + 7 = 10
