GMAT Math : Graphing an ordered pair

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Graphing An Ordered Pair

Which quadrants can include the point   if nonzero numbers  and  have the same sign?

Possible Answers:

Either Quadrant II or Quadrant IV

Either Quadrant I or Quadrant IV

Either Quadrant I or Quadrant II

Either Quadrant II or Quadrant III

Either Quadrant I or Quadrant III

Correct answer:

Either Quadrant I or Quadrant IV

Explanation:

If  and  have the same sign, then , and the point has a positive -coordinate. The sign of  is the same as the common sign of  and . Therefore, only the -coordinate restricts the possibilities.

The points witn positive -coordinates are in Quadrant I and Quadrant IV.

Example Question #2 : Graphing An Ordered Pair

Which quadrant or axis can include the point ?

Possible Answers:

Quadrant III

Quadrant IV

The -axis

Quadrant II

Quadrant I

Correct answer:

Quadrant I

Explanation:

The ordered pair  consists of a positive -coordinate and a positive -coordinate. The only quadrant that consists entirely of positive - and -coordinates is Quadrant I. 

Example Question #3 : Graphing An Ordered Pair

Which quadrant or axis contains the point ?

Possible Answers:

The -axis

Quadrant I

Quadrant III

Quadrant II

The -axis

Correct answer:

The -axis

Explanation:

The ordered pair  consists of a positive -coordinate and a -coordinate of . The only part of the coordinate plane on which all points have a zero -coordinate is the -axis. 

Example Question #4 : Graphing An Ordered Pair

Which of the following ordered pairs is in Quadrant III?

Possible Answers:

Correct answer:

Explanation:

By definition, only Quadrant III contains ordered pairs that have both negative - and -coordinates. 

Example Question #5 : Graphing An Ordered Pair

Which quadrant or axis includes the point ?

Possible Answers:

Quadrant IV

Quadrant I

Quadrant II

The -axis

Quadrant III

Correct answer:

Quadrant II

Explanation:

The ordered pair  has a negative -coordinate and a positive -coordinate. By definition, all ordered pairs with negative -coordinates and a positive -coordinates exist in Quadrant II.

Example Question #6 : Graphing An Ordered Pair

Which quadrant or axis includes the point ?

Possible Answers:

Quadrant I

Quadrant II

The -axis

The -axis

Quadrant III

Correct answer:

The -axis

Explanation:

The ordered pair  has a zero -coordinate and a nonzero -coordinate. By definition, all ordered pairs with zero -coordinates and nonzero -coordinates is on the -axis.

Example Question #7 : Graphing An Ordered Pair

Which of the following ordered pairs is in Quadrant I?

Possible Answers:

None of these coordinates

Correct answer:

Explanation:

 By definition, all ordered pairs with positive -coordinates and positive -coordinates are in Quadrant I. Therefore, the only ordered pair in this quadrant is .

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