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Does line P (not pictured) intersect line segment

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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Apr 12, 2017 5:58 am
NandishSS wrote:Does line P (not pictured) intersect line segment QR in the coordinate plane shown above?

(1) The slope of line P is -1.

(2) The equation of line P is y = -x + 4.
Statement 1: The slope of line P is -1
If line P passes through (1, 3), then it WILL intersect QR.
If line P passes through the origin, then it will NOT intersect QR.
INSUFFICIENT.

Statement 2: The equation of line P is y = -x + 4.
Since the equation of line P is known, we can determine whether it intersects QR.
SUFFICIENT.

The correct answer is B.
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by Jay@ManhattanReview » Wed Apr 12, 2017 6:12 am
NandishSS wrote:Does line P (not pictured) intersect line segment QR in the coordinate plane shown above?

(1) The slope of line P is -1.

(2) The equation of line P is y = -x + 4.

OA:B
Hi NandishSS,

The slope of QR = (3 - 2)/((1 - 2) = 1/-1 = -1

S1: The slope of line P is -1.

We see that the slope of line P = slope of line QR

> If line P is parrallel to line QR, the answer is No.

> If line P is the same as line QR, technically it intersects, so the answer is Yes. I doubt that the GMAT would test this.

Insufficient.

S2: The equation of line P is y = -x + 4.

The slope of line P = -1.

We see that the slope of line P = slope of line QR

Since both the parameters of line P, i.e., the slope and intercept are known, we are sure that it has a unique positioning in the plane; thus, we can determine wheter it intersects or not. Sufficient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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by [email protected] » Wed Apr 12, 2017 9:00 am
Hi NandishSS,

This is a great 'concept' question; if you recognize the concepts involved, then you don't actually have to do any math to get to the correct answer.

We're asked if a line P intersects with the line segment QR. This is a YES/NO question.

1) The slope of line P is -1.

This Fact tells us the slops of line P, but it doesn't tell us exactly where line P is located. Thus, it might intersect the line segment or not.
Fact 1 is INSUFFICIENT

(2) The equation of line P is y = -x + 4.

This Fact gives us the exact equation for line P, so we COULD graph it... and once we did, we'd know definitively whether line P intersected with the line segment or not (and there would be just one answer to the given question).
Fact 2 is SUFFICIENT

Final Answer: B

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