Multiple choice

The number of times 99 is subtracted from 1111 so that the remainder is less than 99 is ____.

  1. 10

  2. 11

  3. 12

  4. 13
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B Correct answer
Explanation

We want to find n such that 1111 - 99n < 99. Solving 1111 - 99 < 99n gives 1012 < 99n, so n > 1012/99, which is approximately 10.22. The smallest integer n is 11.

AI explanation

To find how many times 99 can be subtracted from 1111 while keeping the remainder non-negative, you divide 1111 by 99. The quotient of this division, 1111 / 99 = 11 with a remainder of 22, gives the maximum number of full subtractions. Because the remainder 22 is less than 99, the number of times 99 is subtracted is 11.

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