Multiple choice

M is the largest three-digit number which when divided by 6 and 5 leaves remainder 5 and 3, respectively. What will be 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

M = LCM(6,5)*k + remainder. M = 30k + r. M = 6a + 5 and M = 5b + 3. Solving: M = 30k + 23. Largest 3-digit M is 983. 983 / 11 = 89 remainder 4.

AI explanation

The number M leaves a remainder of 5 when divided by 6 and a remainder of 3 when divided by 5, meaning it can be expressed as 30k minus 1. To find the largest three-digit number of this form, we evaluate 990 minus 1, which gives 989. Dividing 989 by 11 yields a quotient of 89 and a remainder of 4.

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