Question

    The question consists of two statements numbered "I and

    II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. There are three gardens 'X', 'Y' and 'Z'. The average number of trees in 'X', 'Y' and 'Z' is 240. Find the number of trees in 'Y' is how much percent more or less than total number of trees in 'X' and 'Z'. Statement I: Number of trees in 'Z' is 'a' more than the number of trees in 'X' and the number of trees in 'Y' is 'a' more than that in 'Z'. Statement II: The difference between number of trees in 'X' and 'Y' is 60.
    A 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
    B 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
    C The data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
    D The data given in both statements I and II together 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

    Let the number of trees in 'X', 'Y' and 'Z' be 'p', 'q' and 'r' respectively.

    So, sum of the number of trees in 'X', 'Y' and 'Z' = 240 X 3

    So, (p + q + r) = 720

    Statement I:

    Given, (r - p) = a.......(I)

    Or, (q - r) = a..........(II)

    From (i) & (ii), We cannot determine the value of 'a'

    So, data in statement I alone is not sufficient to answer the question.

    Statement II:

    Case I:

    We have, q = p + 60

    Case II:

    We have, q = p - 60

    But we do not have any other data.

    So, data in statement II alone is not sufficient to answer the question.

    From Statement I and Statement II:

    So, 'r' = 240

    So, p + q = 720 - 240 = 480

    And q - p = 60

    So, q = (480 + 60) /2 = 270

    And 'p' = (480 - 60) /2 = 210

    So, total number of trees in 'X' and 'Z' = 210 + 240 = 450

    Number of trees in 'Y' = 270

    So, required percentage = {(450 - 270) /450} X 100 = 40% less

    The data in both statements I and II together is necessary to answer the question.

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