Multiple choice

Which is the largest six-digit number, which when divided by 12, 15, 20, 24 and 30 leaves the remainders 8, 11, 16, 20 and 26, respectively?

  1. 9,99,956

  2. 9,99,960

  3. 9,99,964

  4. 9,99,982
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A Correct answer
Explanation

Find LCM of (12, 15, 20, 24, 30) = 120. The difference between divisor and remainder is constant (12-8=4, 15-11=4, etc). We need the largest 6-digit number N such that N = 120k - 4. Largest 6-digit number is 999999. 999999 / 120 = 8333 with remainder 39. 999999 - 39 = 999960. Subtract 4: 999960 - 4 = 999956.

AI explanation

Observe that the difference between each divisor and its corresponding remainder is 4, meaning if you add 4 to the number, it is perfectly divisible by 12, 15, 20, 24, and 30. Find the least common multiple of these divisors, which is 120. The largest six-digit number is 999999, which when divided by 120 gives a quotient of 8333 and a remainder of 39. Subtract 39 and then 4 to get the required number, which is 999956.

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