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# M23-14

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Math Expert
Joined: 02 Sep 2009
Posts: 44372
M23-14 [#permalink]

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16 Sep 2014, 01:18
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Difficulty:

45% (medium)

Question Stats:

68% (00:46) correct 32% (01:40) wrong based on 84 sessions

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

A. $$k = b$$
B. $$k=b+1$$
C. $$b + k = 0$$
D. $$|k| - 1 = 0$$
E. $$k = -k$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44372
Re M23-14 [#permalink]

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16 Sep 2014, 01:18
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Official Solution:

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

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

For lines to be parallel, their slopes must be equal.

The second equation can be rewritten as $$y=\frac{1}{k}*x-\frac{b}{k}$$ and since the slopes of two lines must be equal, then it must be true that $$k=\frac{1}{k}$$ or $$k^2=1$$ or $$|k|=1$$.

Answer: D
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Joined: 19 Dec 2015
Posts: 28
Re: M23-14 [#permalink]

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23 May 2016, 11:26
This is a very good question in my opinion, should be bumped for further review and discussion
Intern
Joined: 13 Oct 2017
Posts: 40
Re: M23-14 [#permalink]

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17 Oct 2017, 06:42
Hi guys,

I'm still a little confused...I tried plugging in either x or y in order to get the required answer and failed miserably...can Bunuel et al give a more granular explanation please?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 44372
Re: M23-14 [#permalink]

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17 Oct 2017, 07:29
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ttaiwo wrote:
Hi guys,

I'm still a little confused...I tried plugging in either x or y in order to get the required answer and failed miserably...can Bunuel et al give a more granular explanation please?

Thanks

Can you please tell me what is unclear in the solution? Thank you.
_________________
Intern
Joined: 13 Oct 2017
Posts: 40
Re: M23-14 [#permalink]

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17 Oct 2017, 12:28
Bunuel wrote:
ttaiwo wrote:
Hi guys,

I'm still a little confused...I tried plugging in either x or y in order to get the required answer and failed miserably...can Bunuel et al give a more granular explanation please?

Thanks

Can you please tell me what is unclear in the solution? Thank you.

Thanks for your response...I did the second substitution as you said but ended up with:

y = x-b/k ...even tried to expand that even further...and got y= x/k - b/k

In effect I don't know how you ended up with:

y=1/k∗x−b/k

I don't know where the 1/k is coming from.
Math Expert
Joined: 02 Sep 2009
Posts: 44372
M23-14 [#permalink]

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17 Oct 2017, 21:00
ttaiwo wrote:
Bunuel wrote:
ttaiwo wrote:
Hi guys,

I'm still a little confused...I tried plugging in either x or y in order to get the required answer and failed miserably...can Bunuel et al give a more granular explanation please?

Thanks

Can you please tell me what is unclear in the solution? Thank you.

Thanks for your response...I did the second substitution as you said but ended up with:

y = x-b/k ...even tried to expand that even further...and got y= x/k - b/k

In effect I don't know how you ended up with:

y=1/k∗x−b/k

I don't know where the 1/k is coming from.

$$x=b+ky$$;

Re-arrange: $$x - b=ky$$;

Divide by k: $$\frac{x}{k} - \frac{b}{k}=y$$.

Notice that $$\frac{x}{k}$$ is the same as $$\frac{1}{k}*x$$.
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M23-14   [#permalink] 17 Oct 2017, 21:00
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# M23-14

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