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    Question

    Two statements, "I and II," are given below. Decide if the provided data is enough to answer the question.

    What is the value of 'p'?

    Statement I: A group of (p + 16) boys can finish a task in 10 days, while a group of (p + 6) girls can finish the same task in 15 days. Each boy and girl has an efficiency of (3p + 18) and (2p + 32), respectively.

    Statement II: A group of (p - 11) laborers can complete the task in 12 days, while (p - 4) laborers can complete it in 10 days.

    A The data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. Correct Answer Incorrect Answer
    B The data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
    C The data given in both statements I and II together is not sufficient to answer the question. Correct Answer Incorrect Answer
    D The data in statement I alone are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in both statements I and II together is necessary to answer the question. Correct Answer Incorrect Answer

    Solution

    ATQ, Statement I: (p + 16) × 10 × (3p + 18) = (p + 6) × 15 × (2p + 32) Or, 30 × (p + 16) × (p + 6) = 30 × (p + 6) × (p + 16) Or, 30 = 30 We cannot solve the equation further. So, data in statement I alone is not sufficient to answer the question. Statement II: Let the efficiency of each labour be 'a' units/day So, (p - 11) × 12 × a = (p - 4) × 10 × a Or, 6p - 66 = 5p - 20 Or, 'p' = 46 So, data in statement II alone is sufficient to answer the question. Therefore, data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question

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