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

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99951

99921

99941

99931

answer is C.

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Detailed Solution

The greatest number will be multiple LCM of 8 and 9.
LCM of 8 and 9 = 72

The greatest 5-digit number is 99999. Let's divide it by 72.
$99999 \div 72 = (1388 x 72) + 63$
$99999 \div 72 = 9936 + 63$

We want a number that will give us the remainder of 5 when divided by 72.

Therefore, we can add 5 to 9936 to find the number.

$∴$ The number will be: 9941

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