Multiple choice

When 31513 and 34369 are divided by a certain three digit number, the remainders are equal, then the remainder is

  1. 86

  2. 97

  3. 374

  4. 113
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B Correct answer
Explanation

The difference between the numbers is 34369 - 31513 = 2856. The divisor must divide 2856. Factors of 2856 include 294, 357, etc. Checking 3-digit factors, 294 is a candidate. 31513 / 294 gives remainder 97. 34369 / 294 gives remainder 97.

AI explanation

If two numbers leave the same remainder when divided by a certain number, their difference must be perfectly divisible by that number. The difference is 34369 minus 31513 = 2856. The factors of 2856 include 952 and 316. Testing the three-digit divisor 952, 31513 = 952 times 33 + 97, and 34369 = 952 times 36 + 97. The common remainder is 97.

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