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# Lines lm and ln lie in the plane x and intersect one another on the pe

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Math Expert
Joined: 02 Sep 2009
Posts: 47977
Lines lm and ln lie in the plane x and intersect one another on the pe  [#permalink]

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05 Feb 2018, 07:04
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Difficulty:

35% (medium)

Question Stats:

69% (01:19) correct 31% (01:03) wrong based on 70 sessions

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Lines $$l_m$$ and $$l_n$$ lie in the plane x and intersect one another on the perpendicular at point P. Which of the following statements must be true?

(A) A line which lies in plane x and intersects line $$l_m$$ on the perpendicular at a point other than P does not intersect $$l_n$$.

(B) Line segment MN, which does not intersect $$l_m$$, does not intersect $$l_n$$.

(C) If line $$l_o$$ lies in plane y and intersects $$l_m$$ at point P, plane y is perpendicular to plane x.

(D) A circle that lies in plane x and has two points in common with $$l_m$$ also has two points in common with $$l_n$$.

(E) A circle that has exactly one point in common with $$l_m$$ and one point in common with $$l_n$$ also lies in plane x.

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Math Expert
Joined: 02 Aug 2009
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Lines lm and ln lie in the plane x and intersect one another on the pe  [#permalink]

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05 Feb 2018, 08:33
Bunuel wrote:
Lines $$l_m$$ and $$l_n$$ lie in the plane x and intersect one another on the perpendicular at point P. Which of the following statements must be true?

(A) A line which lies in plane x and intersects line $$l_m$$ on the perpendicular at a point other than P does not intersect $$l_n$$.

(B) Line segment MN, which does not intersect $$l_m$$, does not intersect $$l_n$$.

(C) If line $$l_o$$ lies in plane y and intersects $$l_m$$ at point P, plane y is perpendicular to plane x.

(D) A circle that lies in plane x and has two points in common with $$l_m$$ also has two points in common with $$l_n$$.

(E) A circle that has exactly one point in common with $$l_m$$ and one point in common with $$l_n$$ also lies in plane x.

Lines $$l_m$$ and $$l_n$$ are at perpendicular..
so any line perpendicular to any of the lines will be PARALLEL to the second line and will NOT meet that line..
see attached figure ..
let Lo be the line perpendicular to Lm

this is exactly what A says

A
Attachments

lines 90.png [ 5.91 KiB | Viewed 567 times ]

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Lines lm and ln lie in the plane x and intersect one another on the pe &nbs [#permalink] 05 Feb 2018, 08:33
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