Question
If 'x', 'y' and 'z' are integers, then find whether (x +
y - z) is positive or negative. Statement I: (x+y)2Ā = 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.Solution
ATQ, Statement-I: (x+y)2Ā = 64 Or, x + y = Ā± 8 (5-z)2Ā = 9 Or, 5 - z = Ā±3 z = Ć„Ā±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.
