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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 ## On the number line, point R has coordinate r and point T has ##### This topic has 2 expert replies and 0 member replies ### Top Member ## On the number line, point R has coordinate r and point T has ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult On the number line, point R has coordinate r and point T has coordinate t. Is t < 0? (1) -1 < r < 0 (2) The distance between R and T is equal to r^2 OA C Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1295 messages Followed by: 29 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: On the number line, point R has coordinate r and point T has coordinate t. Is t < 0? (1) -1 < r < 0 (2) The distance between R and T is equal to r^2 Source: Official Guide $t\,\,\mathop < \limits^? \,\,0$ $\left( 1 \right)\,\,\, - 1 < r < 0\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {r,t} \right) = \left( { - 0.5,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {r,t} \right) = \left( { - 0.5, - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$ $\left( 2 \right)\,\,\,\left| {r - t} \right| = {r^2}\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {r,t} \right) = \left( {0,0} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {r,t} \right) = \left( { - 1, - 2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \end{gathered} \right.$ $\left( {1 + 2} \right)\,\,\,\,\,\left| {r - t} \right| = {r^2}\,\,\,\,\mathop \Rightarrow \limits^{{\text{squaring}}} \,\,\,\,\,{\left( {r - t} \right)^2} = {r^4}\,\,\,\,\, \Rightarrow \,\,\,\,{r^2} - 2rt + {t^2} = {r^4}\,\,\,\,\,\left( * \right)$ $- 1 < r < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,{r^4} < {r^2}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\, - 2rt + {t^2} = {r^4} - {r^2} < 0$ $\left. \begin{gathered} - 2rt + {t^2} < 0 \hfill \\ {t^2} \geqslant 0 \hfill \\ \end{gathered} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\, - 2rt < 0\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{r\, < \,\,0} \,\,\,t < 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.\,$ 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 ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1770 messages Followed by: 28 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: On the number line, point R has coordinate r and point T has coordinate t. Is t < 0? (1) -1 < r < 0 (2) The distance between R and T is equal to r^2 OA C Source: Official Guide Given: On the number line, point R has coordinate r and point T has coordinate t. Question: Is t < 0? Let's take each statement one by one. (1) -1 < r < 0 We do not have any information about point T. Insufficient. (2) The distance between R and T is equal to r^2. Certainly insufficient. T can be on either side of the number line. Insufficient. (1) and (2) together We know that the coordinate of point R is -1 < r < 0 and the distance between R and T is equal to r^2. Note that if -1 < r < 0, r^2 < |r| Thus, the coordinate of point T must also be negative. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GRE Classes Seattle | GMAT Prep Course Hong Kong | GRE Prep San Francisco | SAT Prep Classes NYC | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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