BrainLab wrote:
Is \(\sqrt{(x + y)}\) an integer?
(1) \(x^3 = 64\)
(2) \(x^2 = y – 3\)
Source: Quant 700 to 800 level questions
(1) Is clearly insufficient, as we don't have any Info about y
(2) Here I made a mistake firstly -> I set \(x^2 + 3 = y\) in the expression and got \(\sqrt{(x^2 + x + 3)}\). I thought, ok, it's a quadratic, so we can get some values for x and it should be sufficient. It was wrong to stop at that point. Discriminant for this expression < 0, which means there are no X-axis intersects.
For the parabola not to cross the x-axis, it must be that the parabola is always above the axis, so when is it greater than zero (above the axis)? Always! Solution: All X
It means that wwe just need to plugin some values for x, and test wheter we get an integer in any case.
It's an integer when x=2, but it is not an integer when x=1 NOT SUFFICIENT
(1) + (2) Sufficient: x=4, y=19, this expression doesn't yield an integer
Answer C
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