Question

    In an office, the number of men

    exceeds the number of women by 13. The average weight of all employees (men and women) is 5 kg higher than the average weight of the women. What is the average weight of the men in the office? Statement I: If there were 8 fewer men and 8 more women, the number of men would be 5% less than the number of women. Statement II: If the average weight of each man increased by 4 kg and the average weight of each woman decreased by 5 kg, the overall average weight of all employees would remain the same. The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
    A The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question. Correct Answer Incorrect Answer
    B The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question. Correct Answer Incorrect Answer
    C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
    D The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer

    Solution

    ATQ, Let the number of women in the office = ‘x’ Then, number of men in the office = (x + 13) Let the average weight of a women in the office = ‘y’ kg Then, average weight of the office = (y + 5) kg Statement I: According to the statement, (x + 13 – 8) = (x + 8) × 0.95 Or, x + 5 = 0.95x + 7.6 Or, x = 2.6 ÷ 0.05 = 52 So, number of women and men in the office is 52 and 65, respectively. So, total weight of the office = (52 + 65) × (y + 5) = (117y + 585) kg Total weight of the women in the office = ‘52y’ kg So, total weight of the men in the office = 117y + 585 – 52y = (65y + 585) kg So, average weight of a men in the office = (65y + 585) ÷ 65 = (y + 9) kg We cannot solve further to obtain the exact value of (y + 9). So, data in statement I alone is not sufficient to answer the question. So, average weight of a boy in the office = (65y + 585) ÷ 65 = (y + 9) kg We cannot solve further to obtain the exact value of (y + 9). So, data in statement I alone is not sufficient to answer the question. Statement II: Let the original average weight a men in the office = ‘z’ kg Then, according to the statement, (x + 13) × (z + 4) + x × (y – 5) = (x + 13) × z + x × y Or, xz + 13z + 4x + 52 + xy – 5x = xz + 13z + xy Or, xz + 13z + 52 + xy – x = xz + 13z + xy Or, xy + 52 – x = xy So, x = 52 So, the number of men and women in the office is 65 and 52, respectively. But with this information alone we cannot determine the average weight of a men in the office. So, data in statement II alone is not sufficient to answer the question. Combining statements I and II: Since, number of women and men in the office is 52 and 65, respectively. We have, 52 × y + 65 × (y + 9) = 52 × (y – 5) + 65 × (y + 9 + 4) Or, 52y + 65y + 585 = 52y – 260 + 65y + 845 Or, 117y + 585 = 117y + 585 This equation cannot be solved any further, So, data in statements I and II together are not sufficient to answer the question.

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