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M23-14

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M23-14  [#permalink]

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New post 16 Sep 2014, 00:18
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A
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D
E

Difficulty:

  35% (medium)

Question Stats:

67% (00:56) correct 33% (01:33) wrong based on 125 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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Re M23-14  [#permalink]

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New post 16 Sep 2014, 00:18
1
2
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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Collection of Questions:
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Re: M23-14  [#permalink]

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New post 23 May 2016, 10:26
This is a very good question in my opinion, should be bumped for further review and discussion :)
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Re: M23-14  [#permalink]

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New post 17 Oct 2017, 05:42
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
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Re: M23-14  [#permalink]

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New post 17 Oct 2017, 06:29
1
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M23-14  [#permalink]

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New post 17 Oct 2017, 11:28
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.
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M23-14  [#permalink]

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New post 17 Oct 2017, 20:00
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 \(\frac{1}{k}*x\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M23-14  [#permalink]

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New post 15 Apr 2018, 02:23
ttaiwo

\(\frac{x-b}{k}\) = \(\frac{x}{k}\) - \(\frac{b}{k}\)

since \(\frac{x}{k}\) = \(\frac{1}{k}\) * \(x\),

\(y = \frac{1}{k} * x - \frac{b}{k}\)
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Re: M23-14 &nbs [#permalink] 15 Apr 2018, 02:23
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