### All GMAT Math Resources

## 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 I or Quadrant IV

Either Quadrant I or Quadrant II

Either Quadrant I or Quadrant III

Either Quadrant II or Quadrant III

Either Quadrant II or Quadrant IV

**Correct answer:**

Either Quadrant I or Quadrant IV

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 II

Quadrant I

Quadrant IV

Quadrant III

The -axis

**Correct answer:**

Quadrant I

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:**

Quadrant III

The -axis

Quadrant I

Quadrant II

The -axis

**Correct answer:**

The -axis

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:**

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 II

Quadrant I

The -axis

Quadrant IV

Quadrant III

**Correct answer:**

Quadrant II

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 III

Quadrant II

Quadrant I

The -axis

The -axis

**Correct answer:**

The -axis

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:**

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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