• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If c is a constant such that the system of equations given a tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## If c is a constant such that the system of equations given a ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 10) Answer: _____(E)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 10) $$?\,\,\,:\,\,\,c\,\,\,{\rm{for}}\,\,{\rm{unique}}\,\,{\rm{solution}}\,\,\left( {x,y} \right)$$ $$c = 0\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x = 1 \hfill \cr \, - 4y = 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {1,0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{refutes}}\,\,\left( A \right),\left( B \right),\left( D \right)$$ $$c = 3\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x - 3y = 1 \hfill \cr \,3x - 4y = 3 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{ \,x - 3y = 1 \hfill \cr \,x - {4 \over 3}y = 1 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{ \,x - 3y = 1 \hfill \cr \,\left( {1 + 3y} \right) - {4 \over 3}y = 1 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{unique}}\,\,{\rm{solution!}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{refutes}}\,\,\left( C \right)$$ The correct answer is (E), by exclusion. We follow the notations and rationale taught in the GMATH method. Regards, Fabio. POST-MORTEM: $$\left\{ \matrix{ \,x - cy = 1 \hfill \cr \,cx - 4y = c \hfill \cr} \right.\,\,\,\,\,\, \cong \,\,\,\,\,\,\left\{ \matrix{ \,x - 1 = cy \hfill \cr \,cx - c = 4y \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\left\{ \matrix{ \,x - 1 = cy \hfill \cr \,c\left( {x - 1} \right) = 4y \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\left\{ \matrix{ \,x - 1 = cy \hfill \cr \,c \cdot cy = 4y \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\left\{ \matrix{ \,x - 1 = cy \hfill \cr \,y\left( {{c^2} - 4} \right) = 0 \hfill \cr} \right.$$ $$\left| c \right| = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{c^2} - 4 = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{infinite}}\,\,{\rm{solutions}}\,\,\,\left( {x,y} \right) = \left( {1 + cy,y} \right)\,\,\,\,\,\,\,\left[ {y\,\,{\rm{free}}} \right]$$ $$\left| c \right| \ne 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{c^2} - 4 \ne 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\{ \matrix{ \,\,y = 0\,\,\,\,\,\,\,\left[ {y\left( {{c^2} - 4} \right) = 0} \right] \hfill \cr \,\,x = 1\,\,\,\,\,\,\,\left[ {x - 1 = cy} \right] \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {x,y} \right){\rm{ = }}\left( {1,0} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{unique}}\,\,{\rm{solution!}}\,\,$$ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 43 first replies
2 Brent@GMATPrepNow 35 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 19 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

149 posts
2 Max@Math Revolution

Math Revolution

93 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

53 posts
4 Ian Stewart

GMATiX Teacher

52 posts
5 GMATGuruNY

The Princeton Review Teacher

32 posts
See More Top Beat The GMAT Experts