Multiple choice

What is the largest 5-digit number, which leaves remainder 7, when divided by 18 as well as by 11?

  1. 99981

  2. 99988

  3. 99997

  4. 99999
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C Correct answer
Explanation

LCM(18, 11) = 198. We need the largest 5-digit number N such that N = 198k + 7. 99999 / 198 = 505.04. 198 * 505 + 7 = 99990 + 7 = 99997.

AI explanation

A number that leaves a remainder of 7 when divided by both 18 and 11 must leave a remainder of 7 when divided by their least common multiple. The least common multiple of 18 and 11 is 198, so we find the largest 5-digit number and divide it by 198. Dividing 99999 by 198 gives a quotient of 505 with a remainder of 9. Subtracting this remainder from 99999 gives 99990, which is the largest multiple of 198; adding 7 gives 99997. The result is 99997.

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