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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 ## If x and y are numbers such that x < - 10 and y > 6, w ##### This topic has 1 expert reply and 0 member replies ### Top Member ## If x and y are numbers such that x < - 10 and y > 6, w ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x and y are numbers such that x < - 10 and y > 6, which of the following expressions is true? I. |x+4| + | y + 4| + | y-4| + |x - 4| > 32 II. |x - 4| + |y + 4| - | x + 4| - | y - 4| < 0 III. |x + 4| + |y + 4| - |x - 4| - |y - 4| = 0 (A) I only (B) II only (C) III only (D) I and III only (E) I, II and III OA D Source: e-GMAT ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1434 messages Followed by: 31 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: If x and y are numbers such that x < - 10 and y > 6, which of the following expressions is true? I. |x+4| + | y + 4| + | y-4| + |x - 4| > 32 II. |x - 4| + |y + 4| - | x + 4| - | y - 4| < 0 III. |x + 4| + |y + 4| - |x - 4| - |y - 4| = 0 (A) I only (B) II only (C) III only (D) I and III only (E) I, II and III Source: e-GMAT $$?\,\,\,:\,\,\,\,{\rm{I,II,III}}\,\,\,{\rm{true}}$$ $$x < - 10\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ \,x + 4 < - 10 + 4 = - 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left| {x + 4} \right| > 6 \hfill \cr \,x - 4 < - 10 - 4 = - 14\,\,\,\,\, \Rightarrow \,\,\,\,\,\left| {x - 4} \right| > 14 \hfill \cr} \right.$$ $$y > 6\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ \,y + 4 > 6 + 4 = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left| {y + 4} \right| > 10 \hfill \cr \,y - 4 > 6 - 4 = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\left| {y - 4} \right| > 2 \hfill \cr} \right.$$ $$\left( {\rm{I}} \right)\,\,\,\left| {x + 4} \right| + \,\left| {y + 4} \right| + \,\left| {y - 4} \right| + \left| {x - 4} \right| > 6 + 10 + 2 + 14 = 32\,\,\,\, \Rightarrow \,\,\,\,{\rm{I}}.\,\,{\rm{TRUE}}\,\,\,\, \Rightarrow \,\,\,\,\left( B \right),\left( C \right)\,\,{\rm{refuted}}$$ $$\left( {{\rm{II}}} \right)\,\,\left| {x - 4} \right| + \,\left| {y + 4} \right| - \,\left| {x + 4} \right| - \left| {y - 4} \right|\,\,\mathop < \limits^? \,\,0\,$$ $${\rm{Take}}\,\,\left( {x,y} \right) = \left( { - 11,7} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\, \Rightarrow \,\,\,\,\,\,\left( E \right)\,\,{\rm{refuted}}$$ $$\left( {{\rm{III}}} \right)\,\,\,\left| {x + 4} \right| + \,\left| {y + 4} \right| - \,\left| {x - 4} \right| - \left| {y - 4} \right|\,\,\, = - \left( {x + 4} \right) + \left( {y + 4} \right) - \left[ { - \left( {x - 4} \right)} \right] - \left( {y - 4} \right) = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{III}}.\,\,{\rm{TRUE}}\,\,\,\, \Rightarrow \,\,\,\,\left( D \right)\,$$ 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free 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 • Award-winning private GMAT tutoring Register now and save up to$200

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