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
OA B
Source: Princeton Review
Two line l and k intersect at a point (4, 3). Is the product
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This one is tricky... nice!BTGmoderatorDC wrote:Two line l and k intersect at 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
Source: Princeton Review
\[\left( {4,3} \right)\,\, \in \,\,\,\left( {{\text{lin}}{{\text{e}}_{\,l}}\,\, \cap \,\,\,{\text{lin}}{{\text{e}}_{\,k}}} \right)\]
\[{\text{slop}}{{\text{e}}_{\,l}}\,\, \cdot \,\,\,{\text{slop}}{{\text{e}}_{\,k}}\,\,\,\mathop = \limits^? \,\,\, - 1\]
(1) Insufficient. We present a GEOMETRIC BIFURCATION in the image attached.
(2) We know line l and line k must have positive slopes (!), therefore the product of their slopes is positive (and not equal to -1)!
The right answer is therefore [spoiler]__(B)___[/spoiler] .
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
![Image](https://s8.postimg.cc/i5xt9nmtd/13_Set18_9m.gif)
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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