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

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by BTGmoderatorDC » Wed Sep 12, 2018 5:10 pm

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E

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

by fskilnik@GMATH » Thu Sep 13, 2018 11:22 am
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
This one is tricky... nice!
\[\left( {4,3} \right)\,\, \in \,\,\,\left( {{\text{lin}}{{\text{e}}_{\,l}}\,\, \cap \,\,\,{\text{lin}}{{\text{e}}_{\,k}}} \right)\]
\[{\text{slop}}{{\text{e}}_{\,l}}\,\, \cdot \,\,\,{\text{slop}}{{\text{e}}_{\,k}}\,\,\,\mathop = \limits^? \,\,\, - 1\]

(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.


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Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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