Multiple choice

The integers 42705 and 43960 when divided by a 3-digit integer 'n' leave the same remainder. What can 'n' be?

  1. 307

  2. 250

  3. 251

  4. 111
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C Correct answer
Explanation

If 42705 and 43960 leave the same remainder when divided by n, then n must divide their difference: 43960 - 42705 = 1255. Factors of 1255 are 1, 5, 251, 1255. The only 3-digit factor is 251.

AI explanation

When two numbers leave the same remainder when divided by n, their difference must be perfectly divisible by n. We subtract the smaller number from the larger number: 43960 minus 42705 equals 1255. We then find which of the provided 3-digit options exactly divides 1255. Dividing 1255 by 251 gives exactly 5 with no remainder. The number n can be 251.

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