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    Question

    The question consists of two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question or not.

    How many students scored at least 40% marks in an exam?

    A total of 720 candidates appeared for the exam. Statement I: One-fifth of the candidates scored 70% or above, and 240 candidates scored more than 20% but less than 40%. Statement II: The number of candidates who scored between 40% and 69% is twice the number of candidates who scored less than 20%.
    A Statement I alone is sufficient to answer the question Correct Answer Incorrect Answer
    B Statement II alone is sufficient to answer the question Correct Answer Incorrect Answer
    C Both statements together are necessary to answer the question Correct Answer Incorrect Answer
    D Either statement I alone or statement II alone is sufficient to answer the question Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Statement I: Number of students those secured 70% marks and above = 1/5 x 720 = 144 240 candidates have secured more than 20% but less than 40% marks in the exam. This statement alone is not sufficient to answer the question. Statement II: In this statement, we don’t have data about the number of students that secured 70 % and above marks. This statement alone is not sufficient to answer the question. On combining (I + II), Number of students those secured those less than 20% marks and those secured marks between 40% and 69% = 720 – 144 – 240 = 336 Number of students those secured between 40% and 69% = 2 x Number of students those secured less than 20% marks Number of students those secured between 40% and 69% = 2/3 x 336 = 224 So number of students those secured at least 40% marks = (40% to 69%) + (70% and above) = 224 + 144 = 368 Statement (I + II) together is sufficient to answer the question. Hence answer is option C

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