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# Two line l and k intersect at a point (4, 3). Is the product of their

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Two line l and k intersect at a point (4, 3). Is the product of their [#permalink]  12 Jan 2015, 11:19
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Question Stats:

52% (02:18) correct 48% (01:17) wrong based on 23 sessions
Two line l and k intersect at a point (4, 3). Is the product of their slopes -1?
(1) x intercepts of line l and k are positive (2) y intercept of line l and k are negative
[Reveal] Spoiler: OA
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Re: Two line l and k intersect at a point (4, 3). Is the product of their [#permalink]  12 Jan 2015, 13:27
Expert's post
Hi PathFinder007,

When dealing with graphing questions on the GMAT, it often helps to draw sketches/pictures to help you stay organized. If you're comfortable with graphing "rules" though, then you don't necessarily need a drawing.

Here, we're told that two lines intercept at the point (4,3). Since we don't know anything about the individual lines (K and L), these lines could have positive slopes, negative slopes, 0 slopes (meaning the lines are horizontal) or undefined slopes (meaning the lines go "straight up and down"). We're asked if the product of their slopes is -1. This is a YES/NO question.

There's a great opportunity here to "rewrite" the question. The ONLY time that the slopes of 2 lines produce a product of -1 is when the two lines are PERPENDICULAR. So this question is essentially asking if lines K and L are perpendicular to one another (meaning they cross and form a 90 degree angle). Perpendicular lines have slopes that can be called "opposite inverse" or "negative reciprocal" (for example, slopes of -2 and +1/2).

Fact 1: The X-intercepts of both lines are positive.

This tells us very little about the two lines. They could have positive or negative slopes (or even an undefined slope).

IF....
X-intercept of K = 1
X-intercept of L = 2
The lines are NOT perpendicular and the answer to the question is NO.

IF.....
X-intercept of K = 1
X-intercept of L = 7
The lines ARE perpendicular and the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: The Y-intercepts of both lines are negative.

This Fact proves that the slopes of BOTH lines are positive (since they cross the Y-axis at a negative number then move UP and to the RIGHT to the point (4,3)), so there is NO WAY for them to cross and be perpendicular. The answer to the question is ALWAYS NO.
Fact 2 is SUFFICIENT.

[Reveal] Spoiler:
B

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Re: Two line l and k intersect at a point (4, 3). Is the product of their [#permalink]  12 Jan 2015, 20:43
Question asks if two lines perpendicular. Yes/No

St1. x intercepts of line l and k are positive. Lines may locate on many options, including perpendicular manner. Answer Yes and No. So, INSUFFICIENT

St.2 y intercept of line l and k are negative. Both lines cannot have negative y interception if they are perpendicular. Answer No. SUFFICIENT

B
Re: Two line l and k intersect at a point (4, 3). Is the product of their   [#permalink] 12 Jan 2015, 20:43
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