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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 ## In the figure above, lines k1 and k2 are parallel to each tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 1 member reply ### Top Member ## In the figure above, lines k1 and k2 are parallel to each ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Manhattan Prep In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x? 1) x = 3z - y 2) (y - z)^2 = 225 The OA is E. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 2008 messages Followed by: 31 members Upvotes: 470 BTGmoderatorLU wrote: Source: Manhattan Prep In the figure above, lines k1 and k2 are parallel to each other, lines l1 and l2 are parallel to each other, and line m passes through the intersection points of k1 with l1 and k2 with l2. What is the value of x? 1) x = 3z - y 2) (y - z)^2 = 225 The OA is E. In the triangle enclosed by angles x, y and z, we have angles: (180 - x), y, and (180 - z). Thus, the sum of all the three angles of the triangle = (180 - x) + y + (180 - z) = 180 => x + y + z = 180. Question: What's the value of x? Let's take each statement one by one. 1) x = 3z - y Plugging-in the value of x in x + y + z = 180, we get (3z - y) + y + z = 180 => z = 45º Can't get the value of x. Insufficient. 2) (y - z)^2 = 225 => y - z = 15 or y - z = -15 Even with the help of x + y + z = 180, we can't get x. Insufficient. (1) and (2) Case 1: y - z = 15 => At z = 45, we have y - z = 15 => y = 60; thus, x + y + z = 180 => x + 60 + 45 = 180 => x = 75 Case 2: y - z = -15 => At z = 45, we have y - z = -15 => y = 30; thus, x + y + z = 180 => x + 30 + 45 = 180 => x = 105 No unique value of x. Insufficient. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review Mehdipatnam | Hyderabad GMAT Prep | Bangalore GMAT Courses | Dilsukhnagar GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1173 messages Followed by: 2 members We are finding the value of x angle z are corresponding angles, the same thing goes for y angle y are corresponding angles at the intersection of line $$k_1$$ ; $$l_1$$ $$and\ \ m_1$$ $$angles\ \left(x+y+2\right)=180\deg ree\left(angle\ on\ a\ straight\ line\right)$$ statement 1 $$x=3z-y$$ we know that $$x+y+z=180\ and\ x=3z-y$$ $$3z-y+y+z=180$$ $$\frac{4z}{4}=\frac{180}{4}$$ $$z=45$$ but x is still unknown. Hence statement 1 is INSUFFICIENT statement 2 $$\left(y-2\right)^2=225$$ square rooting both sides $$\sqrt{\left(y-2\right)^2}=\sqrt{225}$$ $$y-2=\pm15$$ We cannot determine the value of x with the information provided in statement 2 Hence 2 is INSUFFICIENT. Combining statement 1 and 2 together $$z=45\ and\ y-z=\pm15$$ $$y=60\deg ree\ \ OR\ y=30\deg ree$$ $$x+y+z=180\deg ree$$ $$x=180-y-z$$ $$x=180-45-60\ \ OR\ x=180-45-30$$ $$x=75\ \ O\ R\ x=105$$ There are more than one solution Hence the two statements together are not SUFFICIENT. $$answer\ is\ option\ E$$ • 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 Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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