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Math Expert V
Joined: 02 Sep 2009
Posts: 55668

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Difficulty:   25% (medium)

Question Stats: 70% (01:00) correct 30% (01:38) wrong based on 146 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. $$k = -k$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 55668

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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 $$|k|=1$$.

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This is a very good question in my opinion, should be bumped for further review and discussion Intern  B
Joined: 13 Oct 2017
Posts: 38

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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 V
Joined: 02 Sep 2009
Posts: 55668

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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.
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Intern  B
Joined: 13 Oct 2017
Posts: 38

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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 V
Joined: 02 Sep 2009
Posts: 55668

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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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Intern  B
Joined: 31 Mar 2018
Posts: 7
Location: India
Concentration: Sustainability, General Management
Schools: Erasmus '20
GMAT 1: 550 Q44 V23 GMAT 2: 660 Q44 V38 GMAT 3: 710 Q47 V41 GPA: 3
WE: Architecture (Other)

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ttaiwo

$$\frac{x-b}{k}$$ = $$\frac{x}{k}$$ - $$\frac{b}{k}$$

since $$\frac{x}{k}$$ = $$\frac{1}{k}$$ * $$x$$,

$$y = \frac{1}{k} * x - \frac{b}{k}$$ Re: M23-14   [#permalink] 15 Apr 2018, 03:23
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