Multiple choice

Find the greatest number of four digits which when divided by $8, 9$ and $10$ leaves $5$ as remainder in each case.

  1. $9730$
  2. $9725$
  3. $9715$
  4. $9995$
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B Correct answer
Explanation

LCM of 8, 9, 10 is 360. The largest 4-digit number is 9999. 9999 / 360 = 27 with remainder 279. 9999 - 279 = 9720. Adding the remainder 5 gives 9725.

AI explanation

The least common multiple of 8, 9 and 10 is 360. The greatest four-digit number is 9999, and dividing 9999 by 360 gives a quotient of 27 and a remainder of 279. Subtracting this remainder from 9999 gives 9720, and adding the required remainder of 5 yields 9725.

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