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M23 Q14

Author Message
Joined: 20 Aug 2009
Posts: 311
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 15

Kudos [?]: 124 [0], given: 69

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23 Feb 2010, 12:57
I want to discuss following question:

If line $$y = kx + b$$ is parallel to line $$x = b + ky$$ , which of the following must be true?

A) $$k = b$$
B) $$k = 1$$
C) $$b + k = 0$$
D) $$|k| - 1 = 0$$
E) $$k = -k$$

[Reveal] Spoiler: OA:
D

[Reveal] Spoiler: OE:
For lines to be parallel, their slopes must be equal. The second equation can be rewritten as $$y = \frac{1}{k}*x - \frac{b}{k}$$ . Because slopes must be equal, $$k = \frac{1}{k}$$ or $$k^2 = 1$$ or $$|k| = 1$$ .

Obviously the slopes of the lines should be the same. But what about y-intercepts? If the slopes of two lines are same AND y-intercepts are also the same we in fact have the same line, not two parallel lines.

From equality of slopes we establish, that $$|k|=1$$, but I also thought that maybe -
$$b\neq-\frac{b}{k}$$
$$k\neq-1$$
$$k=1$$

What do you think?
Senior Manager
Joined: 13 Dec 2009
Posts: 263
Followers: 10

Kudos [?]: 161 [0], given: 13

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13 Mar 2010, 11:58
shalva wrote:
I want to discuss following question:

If line $$y = kx + b$$ is parallel to line $$x = b + ky$$ , which of the following must be true?

A) $$k = b$$
B) $$k = 1$$
C) $$b + k = 0$$
D) $$|k| - 1 = 0$$
E) $$k = -k$$

[Reveal] Spoiler: OA:
D

[Reveal] Spoiler: OE:
For lines to be parallel, their slopes must be equal. The second equation can be rewritten as $$y = \frac{1}{k}*x - \frac{b}{k}$$ . Because slopes must be equal, $$k = \frac{1}{k}$$ or $$k^2 = 1$$ or $$|k| = 1$$ .

Obviously the slopes of the lines should be the same. But what about y-intercepts? If the slopes of two lines are same AND y-intercepts are also the same we in fact have the same line, not two parallel lines.

From equality of slopes we establish, that $$|k|=1$$, but I also thought that maybe -
$$b\neq-\frac{b}{k}$$
$$k\neq-1$$
$$k=1$$

What do you think?

It should be D, cos y intercept can be equal as it is given that lines are parallel but it is not given that lines are not equal.
_________________

My debrief: done-and-dusted-730-q49-v40

Re: M23 Q14   [#permalink] 13 Mar 2010, 11:58
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M23 Q14

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