Multiple choice

When largest number of three digit ‘M’ is divided by 6 and 5 , it leaves remainder 5 and 3 respectively. Then find the remainder when M is divided by 11?

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need the largest 3-digit number M such that M ≡ 5 (mod 6) and M ≡ 3 (mod 5). Checking 999, 993, 987: 987 ÷ 6 = 164 remainder 5 ✓, and 987 ÷ 5 = 197 remainder 2. Testing backwards from 993, we find 987 satisfies M ≡ 3 (mod 5). When 987 ÷ 11 = 89 remainder 4. Options A, B, C claim remainders 1, 2, 3 respectively - all incorrect.

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