Multiple choice

Find the largest 5 digit number which when divided by 8 leaves a remainder of 3 and when divided by 9 leaves a remainder of 1.

  1. 99845

  2. 99864

  3. 99936

  4. 99955
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D Correct answer
Explanation

We need a number N such that N = 8k + 3 and N = 9m + 1. This implies N is congruent to 3 mod 8 and 1 mod 9. Testing the largest 5-digit numbers near 99999, 99955 divided by 8 gives 12494 remainder 3, and 99955 divided by 9 gives 11106 remainder 1.

AI explanation

The largest 5 digit number is 99999. Dividing 99999 by 72 gives a quotient of 1388 with a remainder of 63, so the largest multiple of both 8 and 9 is 99936. Adding 19 to 99936 provides a remainder of 3 when divided by 8 and a remainder of 1 when divided by 9, giving the result 99955.

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