Multiple choice

Find the greatest number of 5 digits, that will give us a remainder of 5, when divided by 8 and 9, respectively.

  1. 99931

  2. 99941

  3. 99725

  4. None of these
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B Correct answer
Explanation

The LCM of 8 and 9 is 72. We need a 5-digit number N such that N = 72k + 5. The largest 5-digit number is 99999. 99999 / 72 = 1388 with remainder 63. So 72 * 1388 + 5 = 99936 + 5 = 99941.

AI explanation

The number must leave a remainder of 5 when divided by both 8 and 9, meaning it must leave a remainder of 5 when divided by their least common multiple. The least common multiple of 8 and 9 is 72. The greatest five-digit number is 99941, which when divided by 72 gives a quotient of 1388 and a remainder of 5.

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