The correct answer is (C). **Step-by-step breakdown:** **Objective:** Determine the unique numerical value of $x$. **Analyze Statement (I) alone:** Statement (I) provides the equation: $x^2 - 7x + 12 = 0$. This is a quadratic equation, which can be solved by factoring: $(x-3)(x-4) = 0$ This yields two possible values for $x$: $x=3$ or $x=4$. Since there are two possible values for $x$, Statement (I) alone is not sufficient to determine a unique value for $x$. **Analyze Statement (II) alone:** Statement (II) provides the inequality: $x > 3.5$. This inequality indicates that $x$ can be any real number greater than 3.5 (e.g., 3.6, 4, 5.1, etc.). Since there are infinitely many possible values for $x$ that satisfy this condition, Statement (II) alone is not sufficient to determine a unique value for $x$. **Analyze Statements (I) and (II) together:** From Statement (I), we know that $x$ can be either $3$ or $4$. From Statement (II), we know that $x$ must be greater than $3.5$. Let's evaluate each possible value from Statement (I) against the condition in Statement (II): 1. If $x=3$: Is $3 > 3.5$? No, this is false. 2. If $x=4$: Is $4 > 3.5$? Yes, this is true. By combining both statements, the only value of $x$ that satisfies both conditions is $x=4$. Therefore, both Statements (I) and (II) together are sufficient to determine a unique value for $x$. **Conclusion:** Statement (I) alone is not sufficient. Statement (II) alone is not sufficient. Statements (I) and (II) together are sufficient. This matches option (C).