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Lines m and n are parallel and 12 inches apart. Two distinct lines p 04 Jul 2022, 01:30
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Lines m and n are parallel and 12 inches apart. Two distinct lines p and q are parallel to m, and are each twice as far from m as from n. If all the four lines lie in the same plane, what is the distance, in inches, between p and q?

(A) 8
(B) 12
(C) 16
(D) 20
(E) 24


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Lines m and n are parallel and 12 inches apart. Two distinct lines p 04 Jul 2022, 04:04
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All four lines are parallel.
Two distinct lines p and q are parallel to m, and are each twice as far from m as from n.
One of the distinct lines is between m and n: its distance to m is 8, and its distance to n is 4.
The other is outside the range between m and n: it is closer to n at the distance of 12. (therefore, its distance to m is 24)

The distance between p and q is 4+12=16
The answer is thus (C).
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Lines m and n are parallel and 12 inches apart. Two distinct lines p 04 Jul 2022, 04:17
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zhanbo
All four lines are parallel.
Two distinct lines p and q are parallel to m, and are each twice as far from m as from n.
One of the distinct lines is between m and n: its distance to m is 8, and its distance to n is 4.
The other is outside the range between m and n: it is closer to n at the distance of 12. (therefore, its distance to m is 24)

The distance between p and q is 4+12=16
The answer is thus (C).
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Hi Zhanbo - i cant visualise how this look, would you mind sharing how the lines are visualized on a plane?Thanks a lot! :)
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Lines m and n are parallel and 12 inches apart. Two distinct lines p 04 Jul 2022, 08:03
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rdrdrd1201
zhanbo
All four lines are parallel.
Two distinct lines p and q are parallel to m, and are each twice as far from m as from n.
One of the distinct lines is between m and n: its distance to m is 8, and its distance to n is 4.
The other is outside the range between m and n: it is closer to n at the distance of 12. (therefore, its distance to m is 24)

The distance between p and q is 4+12=16
The answer is thus (C).

Hi Zhanbo - i cant visualise how this look, would you mind sharing how the lines are visualized on a plane?Thanks a lot! :)
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Sure. Please see the attached file for the visualization.

This is the very first post of mine that includes a picture. :-)
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File comment: Four lines
Demo.JPG
Demo.JPG [ 17.01 KiB | Viewed 1900 times ]

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Lines m and n are parallel and 12 inches apart. Two distinct lines p 05 Jul 2022, 08:37
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Answer would be 'C', because one line should be in between m and n, and the other should be below n, Because there is only one possibility for distance of the line from m to be twice that of n, if the line should be in between m and n.

Let's consider the line between m and n as p, and the distance between p and n as z.

Since, m - n = 12, z+2z = 12 (as pm = 2pn)
3z = 12
z = 4

Now as q is below n,

Let's consider the distance as x,

distance between m and q is 2x,

therefore, 2x - x = 12
=> x = 12

therefore, the distance between p and q = 12 + 4 = 16. Option C.
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