Bunuel wrote:

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Point (x, y) lies in which quadrant of the rectangular coordinate system shown in the figure below?

(1) x = –2

(2) x + y < 0

Kudos for a correct solution. OFFICIAL SOLUTION:This data sufficiency question concerns the quadrant plane of coordinate geometry fame. You need information that places the point in one specific quadrant of the plane. You can do that if you know whether each coordinate is negative or positive.

Statement (1) tells you that x is negative, so you know that the point is to the left of the coordinate plane. But you don’t know the value of y, so you don’t know which of the left quadrants it is in. Eliminate A and D and check out statement (2).

You could solve the equation in statement (2) to discover that either y < –x or x < –y, but neither of those solutions tells you whether the values are definitely positive or negative. So eliminate B because statement II isn’t sufficient. Now consider the two statements together.

When you combine the information in the two equations, you get that x = –2 and that y < 2:

x + y < 0

–2 + y < 0

y < 2

You know the value of x, but you still have a range of values for y that could be either positive or negative. Therefore, you still don’t know exactly which quadrant the point is in. The two statements together are insufficient to answer the question, so you can eliminate C.

E is the correct answer.

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