A boy multiplied 423 by a number and obtained 65589 as his answer. If both the fives in the answer are wrong and all other figures are correct, the correct answer is:

### Concept & Logic This is a number system problem testing divisibility and pattern recognition. Since we know the incorrect answer (65589) has exactly three correct digits (6, 8, and 9) in their correct place values, the true answer must be in the format $6\_\_89$. Furthermore, the true answer must be perfectly divisible by the original multiplicand, 423. ### Step-by-Step Solution * **Analyze the structure of the correct answer:** The answer must look like $6\_\_89$. Let the unknown multiplier be $x$. $423 \times x = 6\_\_89$. * **Determine the unit digit of the multiplier:** The product ends in 9. The multiplicand (423) ends in 3. The only single digit that yields a 9 when multiplied by 3 is 3 ($3 \times 3 = 9$). Therefore, the multiplier $x$ must end in 3 (e.g., 143, 153). * **Test the given options:** Since all options fit the pattern (they begin with 6 and end with 89), we simply divide each by 423 to see which yields a whole number. Option (a) 60489: $\frac{60489}{423} = 143$ (Exact match) Option (b) 61189: $\frac{61189}{423} \approx 144.6$ Option (c) 62189: $\frac{62189}{423} \approx 147.01$ Option (d) 62389: $\frac{62389}{423} \approx 147.49$ ### Exam Strategy & Shortcut Use the options to your advantage. Since the answer must be perfectly divisible by 423, you can use the digital root (sum of digits) to quickly verify divisibility by 9 (since 423 is divisible by 9, as $4+2+3=9$). Test option (a) 60489: $6+0+4+8+9 = 27$ (Divisible by 9). Test option (b) 61189: $6+1+1+8+9 = 25$ (Not divisible by 9). Test option (c) 62189: $6+2+1+8+9 = 26$ (Not divisible by 9). Test option (d) 62389: $6+2+3+8+9 = 28$ (Not divisible by 9). Option (a) is the only mathematically possible answer. ### Common Pitfall Students often try to guess the missing digits by trial and error without testing the provided options, which wastes valuable time. Always leverage the multiple-choice format for divisibility checks. ### Final Answer **Therefore, the correct answer is 60489.**