Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. An Integer x, when divided by 4 or 6, results in a remainder of 1. Which of the following cannot be a remainder when the same number is divided by 9?

Explanation: (A) The number x must be of the form \(12k + 1\) (since LCM of 4 and 6 is 12). If k=1, x=13. \(13 \div 9\) has remainder 4. If k=2, x=25. \(25 \div 9\) has remainder 7. If k=3, x=37. \(37 \div 9\) has remainder 1. If k=4, x=49. \(49 \div 9\) has remainder 4. If k=5, x=61. \(61 \div 9\) has remainder 7. If k=6, x=73. \(73 \div 9\) has remainder 1. The remainders are 1, 4, 7. Thus, 2 and 3 cannot be a remainder when the same number is divided by 9. Since 2 is the first option, A is the answer.