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    Question

    In each of the following questions, two statements or three statements are given. You are expected to solve them and determine which statement or combination of statements is sufficient to answer the question.

    A box contains red and blue marbles. What is the ratio of red marbles to blue marbles in the box?

    Statements I:  The number of red marbles is 40% of the total number of marbles in the box.

    Statements II:  There are 30 more blue marbles than red marbles.

    A Statement 1 alone is sufficient, but statement 2 alone is not sufficient. Correct Answer Incorrect Answer
    B Statement 2 alone is sufficient, but statement 1 alone is not sufficient. Correct Answer Incorrect Answer
    C Both statements together are sufficient, but neither alone is sufficient. Correct Answer Incorrect Answer
    D Each statement alone is sufficient. Correct Answer Incorrect Answer
    E Statements 1 and 2 together are not sufficient. Correct Answer Incorrect Answer

    Solution

    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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