Point (P, Q) is in the coordinate plane. Is P > Q? (1) P

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Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

OA B

Source: Magoosh

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by Jay@ManhattanReview » Tue Sep 25, 2018 9:08 pm

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BTGmoderatorDC wrote:Point (P, Q) is in the coordinate plane. Is P > Q?

(1) P is positive.
(2) Point (P, Q) above on the line y = x + 1.

OA B

Source: Magoosh
We have to determine whether s P > Q.

Let's take each statement one by one.

(1) P is positive.

Certainly many possibilities. For example (2, 2), (2, 3) and (3, 2). No unique answer. insufficient.

(2) Point (P, Q) is above the line y = x + 1.

The line y = x + 1 passes through I, II and III quadrants and the area above the line y = x + 1 would be represented by the inequality y > x + 1. To be sure that it is not y < x + 1, you may plug-in the coordinates of origin (0, 0) in y < x + 1; we see that 0 < 0 + 1 => 0 < 1 is true, it means that y < x + 1 represents the area below the line y = x + 1 since the origin is below the line; thus, the area above the line y = x + 1 is given by y > x + 1.

Since y > x + 1, we have y - x > 1 => y > x. It means that any point above the line y = x + 1 would have its y-coordinate greater than the x-coordinate. Or Q > P. The answer is NO -- a unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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