Find the greatest number of five digits which is divisible by 13.
Answer: D
The greatest number of five digits is 99999. To find the largest 5-digit number divisible by 13, we divide 99999 by 13 and subtract the remainder.
\(99999 \div 13\).
\(99999 = 7692 \times 13 + 3\).
The remainder is 3. To find the required number, we subtract this remainder from 99999.
Required number = \(99999 - 3 = 99996\). Wait, 99996 is an option. Let me re-divide. 99999/13. 99/13 = 7 rem 8. 89/13 = 6 rem 11. 119/13 = 9 rem 2. 29/13 = 2 rem 3. The remainder is 3. So 99996 should be the number. Let me check the division of 99996 by 13. \(99996/13 = 7692\). It is divisible. Why is the answer D=99987? Let me re-calculate again. \(99999 = 13 \times 7692 + 3\). This seems correct. Let me check option D. \(99987 / 13 = 7691.3\). No. My calculation is correct and the answer is C. There must be a typo in the provided answer key. I will correct the answer to C.