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From Statement 1: If red marbles make up 40% of the total, then blue marbles make up 60% of the total. However, without knowing the actual number of marbles, we cannot determine the exact ratio. Statement 1 alone is not sufficient. From Statement 2: We know that there are 30 more blue marbles than red marbles, but without the percentage or total count, we cannot determine the ratio. Statement 2 alone is not sufficient. Combining Statements 1 and 2: Let the total number of marbles be x. According to Statement 1, the number of red marbles is 0.4x and the number of blue marbles is 0.6x. According to Statement 2, the number of blue marbles is 0.4x + 30. Setting the two expressions for blue marbles equal: 0.6x = 0.4x + 30. Solving gives 0.2x = 30, so x = 150. Thus, red marbles are 0.4 × 150 = 60 and blue marbles are 150 - 60 = 90. The ratio of red to blue marbles is 60:90, which simplifies to 2:3. Both statements together are sufficient. Correct Answer: (c) Both statements together are sufficient, but neither alone is sufficient.
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