When I first looked at this question, especially the bit on √xy=xy , I knew that plugging in the values of 1 and 0 for xy would be the fastest approach since these are the only two values that satisfy the equation given.
Remember that if the question says √xy=xy or something similar, it’s telling you that the values under the root can be 1 or 0.
So if √xy=xy , it means xy = 1 or xy = 0. If xy=1, x=y=1 or x=y=-1; if xy=0, at least one of the numbers is 0.
With this, let us analyse the statements.
From statement I alone, we know x = -\(\frac{1}{2}\). If xy=1, value of y will be -2 and if xy=0, value of y will be 0. Since we do not know the exact value of xy, statement I alone is insufficient to find the value of y and hence the value of x+y.
Answer options A and D can be eliminated. Possible answer options are B, C or E.
From statement II alone, we know that y is not equal to 0. This eliminates the possibility of y being 0. However, we still do not know the exact values of x and y and hence cannot find the value of x+y. Statement II alone is insufficient.
Answer option B can be eliminated. Possible answer options are C or E.
Combining both statements I and II, we have the following:
From statement II alone, we know that xy≠0. Coupling this with the data given in the question, we can say that xy HAS TO be equal to 1.
From statement I alone, we know that x = -\(\frac{1}{2}\).
Since xy=1 and x=-\(\frac{1}{2}\), we can say that y=-2. Since we know x and y uniquely, we can calculate the value of x+y. The combination of statements is sufficient.
The correct answer option is C.
Hope that helps!
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