Consider the Question and two Statements given below : Question : Is x an integer? Statement- 1 : x / 3 is not an integer. Statement- 2 : 3 xis an integer. Which one of the following is correct in respect of the Question and the Statements?

The question asks whether x is an integer. Statement 1: x / 3 is not an integer. If x = 1, then x/3 = 1/3, which is not an integer. In this case, x is an integer. If x = 0.5, then x/3 = 0.5/3 = 1/6, which is not an integer. In this case, x is not an integer. Since Statement 1 allows for both 'x is an integer' and 'x is not an integer', it is not sufficient. Statement 2: 3x is an integer. If x = 1, then 3x = 3, which is an integer. In this case, x is an integer. If x = 1/3, then 3x = 3 * (1/3) = 1, which is an integer. In this case, x is not an integer. Since Statement 2 allows for both 'x is an integer' and 'x is not an integer', it is not sufficient. Combining Statement 1 and Statement 2: We need to find if x is an integer given that x/3 is not an integer AND 3x is an integer. Case 1: Let x = 1. Statement 1: 1/3 is not an integer (True). Statement 2: 3 * 1 = 3 is an integer (True). In this case, x is an integer. Case 2: Let x = 1/3. Statement 1: (1/3) / 3 = 1/9 is not an integer (True). Statement 2: 3 * (1/3) = 1 is an integer (True). In this case, x is not an integer. Since both statements together still allow for scenarios where x is an integer (e.g., x=1) and scenarios where x is not an integer (e.g., x=1/3), they are not sufficient to definitively answer whether x is an integer. Therefore, both Statement 1 and Statement 2 are not sufficient to answer the question. The final answer is D