DSQ: Graphing an ordered pair - GMAT Quantitative Reasoning

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Question

What quadrant contains the point , where ?

Statement 1:

Statement 2:

Answer

Statement 1 alone tells you that and are of the same sign, so the point is in Quadrant I (both positive) or Quadrant III (both negative).

Statement 2 tells you that any of the following hold:

is positive and is negative - example:

is negative and is negative - example:

is positive and is positive - example:

This places the point in any quadrant except Quadrant II (where is negative and is positive).

The two statements together only eliminate two quadrants and leave both Quadrant I and Quadrant III as possibilities.

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Question

Graph the point .

I) is in quadrant IV.

II) .

Answer

Graph the point (a,b)

I) (a,b) is in quadrant 4

II)

To graph (a,b) we need to know a and b

I) Tells us which quadrant the point is in. In quadrant 4, the x value is positive and the y value must be negative.

II) Lets us find the following:

So the only possible location of is .

Therefore, both statements are needed to answer the question.

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