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    Question

    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.

    If 'x', 'y' and 'z' are integers, then find whether (x +

    y - z) is positive or negative. Statement I: (x+y)2 = 64 and (5 - z)2 = 9 Statement II : xy - yz - zx = 11
    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, Statement-I: (x+y)2 = 64 Or, x + y = ± 8 (5-z)2 = 9 Or, 5 - z = ±3 z = å±3 z = 2/8 For, x + y = 8 For, x + y = -8 (x + y - z) = (- 8 - 2) or 8 - 8) = -10, -16 So, data in statement I alone is not sufficient to answer the question. Statement II: (x + y - = x2 + y2 + z2 + 2xy - 2yz - 2zx Or, (x + y - z = x2 + y2 + z2 + 2(xy - yz - zx) Or, (x + y - z = x2 + y2 + z2 + 22 [As, xy - yz - zx = 11] Which is inconclusive So, data in statement II alone is not sufficient to answer the question. Combining statement I and II: We can't find the value of x, y and z. So, data given in both statements I and II together are not sufficient to answer the question.

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