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# The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7086
GMAT 1: 760 Q51 V42
GPA: 3.82
The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio  [#permalink]

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27 Sep 2018, 00:59
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45% (medium)

Question Stats:

58% (01:26) correct 42% (02:02) wrong based on 35 sessions

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[Math Revolution GMAT math practice question]

The $$2$$ lines $$x+2y=3, 2x+py=q$$ have infinitely many points of intersection in the xy-plane. Which of the following could be the value of $$p$$?

$$A. 0$$
$$B. 1$$
$$C. 2$$
$$D. 3$$
$$E. 4$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 17 May 2018 Posts: 48 Re: The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio [#permalink] ### Show Tags 27 Sep 2018, 03:03 If the two lines have an infinite number of intersections, then they must be overlapped. Their equations should then be the same. Equation of line 1, isolating y: y=-x/2 + 3/2 Equation of line 2, isolating y: y=-2x/p + q/p We want the same slope so p should be 4 in order to obtain y=-x/2 + q/4 _________________ ¿Tienes que presentar el GMAT y no sabes por dónde empezar? ¡Visita GMAT para Principiantes y recibe el curso completo gratis! GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 902 Re: The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio [#permalink] ### Show Tags 27 Sep 2018, 08:34 MathRevolution wrote: The $$2$$ lines $$x+2y=3, 2x+py=q$$ have infinitely many points of intersection in the xy-plane. Which of the following IS the value of $$p$$? $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. 4$$ $$? = p$$ From the question stem, we know both lines (each represented by one of the equations) must coincide (*), hence: $$\left\{ \begin{gathered} \,x + 2y = 3\,\,\,\left( { \cdot 2} \right) \hfill \\ 2x + py = q \hfill \\ \end{gathered} \right.\,\,\,\,\,\, \sim \,\,\,\,\,\,\left\{ \begin{gathered} \,2x + 4y = 6 \hfill \\ 2x + py = q \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,? = p = 4\,\,\,\,\,\,\,\left( {{\text{and}}\,\,q = 6} \right)$$ This solution follows the notations and rationale taught in the GMATH method. Regards, fskilnik. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Manager Joined: 14 Jun 2018 Posts: 223 Re: The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio [#permalink] ### Show Tags 27 Sep 2018, 10:26 Infinite intersection means they are on top of each other , which in turn means their slope is the same. Option E Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7086 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio [#permalink] ### Show Tags 30 Sep 2018, 22:56 => If the $$2$$ lines have infinitely many points of intersection, their equations must specify the same straight line. The equation $$x+2y=3$$ is equivalent to $$2x+4y=6.$$ So, $$p = 4$$ and $$q = 6$$. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: The 2 lines x+2y=3, 2x+py=q have infinitely many points of intersectio   [#permalink] 30 Sep 2018, 22:56
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