If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does...

[BTGmoderatorLU]

Source: Manhattan Prep

If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie?

1) (p, q) lies in quadrant IV.
2) (q, -p) lies in quadrant III.

The OA is D

[Jay@ManhattanReview]

Source: Manhattan Prep

X-Ycoordinategrid.jpg

If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie?

1) (p, q) lies in quadrant IV.
2) (q, -p) lies in quadrant III.

The OA is D

Let's take each statement one by one.

1) (p, q) lies in quadrant IV.

Since the point (p, q) lies in quadrant IV, p must be positive and q must be negative. We can rewrite the coordinates as (|p|, –q|).

Thus, (p, p – q) = (|p|, (|p| –*–|q|) = (|p|, (|p|+|q|). We see that both x-coordinate and y-coordinate are positive, thus, the point (p, p – q) lies in quadrant I. Sufficient.

2) (q, –p) lies in quadrant III.

Since the point (q, –p) lies in quadrant III, q must be negative and p must be positive. We can rewrite the coordinates as (–|q|, –|p|).

(p, p – q) = (|p|, (|p| –*–|q|) = (|p|, (|p| + |q|). As with Statement 1, we see that both x-coordinate and y-coordinate are positive, thus, the point (p, p – q) lies in quadrant I. Sufficient.

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review

Locations: Manhattan Review Hyderabad | GMAT Prep Bangalore | GRE Prep Chennai | Himayatnagar GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.