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    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 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, 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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