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    Question

    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%. 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.
    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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