If line k in the xy-coordinate plane has the equation Ax + B

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Nov 14, 2018 9:53 pm

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If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B

(2) C = 4B

OA A

Source: Magoosh

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Source: Beat The GMAT — Data Sufficiency | Wed Nov 14, 2018 9:53 pm

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by Brent@GMATPrepNow » Thu Nov 15, 2018 7:14 am

BTGmoderatorDC wrote:If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B
(2) C = 4B

Given: Line k has the equation Ax + By = C

Target question: What is the slope of line k ?
This is a good candidate for rephrasing the target question.
Let's take the given equation Ax + By = C and rewrite it in slope y-intercept form, y = mx + b, where m = slope and b = y-intercept

GIVEN: Ax + By = C
Subtract Ax from both sides to get: By = -Ax + C
Divide both sides by B to get: y = -Ax/B + C/B
Rewrite to get: y = (-A/B)x + C/B
With the line's equation written in this form, we can see that line k has slope -A/B and y-intercept C/B
So, we can REPHRASE our target question....
REPHRASED target question: What is the value of -A/B ?

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: A = 2B
Divide both sides by B to get: A/B = 2
This means -A/B = -2
So, the answer to the REPHRASED target question is -A/B = -2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: C = 4B
Since we have no information about A, there's no way to determine the value of -A/B
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Nov 15, 2018 9:25 am

BTGmoderatorDC wrote:If line k in the xy-coordinate plane has the equation Ax + By = C, what is the slope of line k ?

(1) A = 2B

(2) C = 4B
Source: Magoosh

Important: from the stem we know (implicitly) that line k HAS a slope, i.e., line k is non-vertical, i.e., B is nonzero.
$$Ax + By = C\,\,\,\,\,\mathop \Leftrightarrow \limits^{B\,\, \ne \,\,0} \,\,\,y\,\, = - {A \over B}\left( x \right)\,\, + \,\,{C \over A}$$
$$? = - {A \over B}$$
$$\left( 1 \right)\,\,\,A = 2B\,\,\,\,\mathop \Rightarrow \limits^{B\,\, \ne \,\,0} \,\,\,\,\,? = - {A \over B} = - 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,\,C = 4B\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {A,B,C} \right) = \left( {1,1,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{?}}\,\,\,{\rm{ = }}\,\, - 1\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {A,B,C} \right) = \left( {2,1,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{?}}\,\,\,{\rm{ = }}\,\, - 2\,\, \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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