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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 ## Is z equal to the median of the three positive integers, x, ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Is z equal to the median of the three positive integers, x, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Is z equal to the median of the three positive integers, x, y, and z? (1) x < y + z (2) y = z OA B Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: Is z equal to the median of the three positive integers, x, y, and z? (1) x < y + z (2) y = z Source: GMAT Prep $x,y,z\,\, \geqslant 1\,\,{\text{ints}}$ ${\text{z}}\,\,\mathop = \limits^? \,{\text{Med}}\,\left( {x,y,z} \right)$ $\left( 1 \right)\,\,x < y + z\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {x,y,z} \right) = \left( {1,1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,\left( {x,y,z} \right) = \left( {1,2,3} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \end{gathered} \right.$ $\left( 2 \right)\,\,y = z\,\,\,\, \Rightarrow \,\,\,{\text{Med}}\,\left( {x,y,z} \right) = \,\,\,{\text{Med}}\,\left( {x,z,z} \right) = z\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle$ (The last equality is true if x is equal to z, and it is also true if x is not equal to z.) 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: 1946 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: Is z equal to the median of the three positive integers, x, y, and z? (1) x < y + z (2) y = z OA B Source: GMAT Prep Given: x, y, and z are positive integers. Question: Is z equal to the median of x, y, and z? Let's take each statement one by one. (1) x < y + z Case 1: Say x = y = z = 2. Median = 2 = z. The answer is Yes, z is the median of x, y, and z. Case 2: Say x = 2, y = 1, and z = 3. Median = 2 = x. The answer is No, z is not the median of x, y, and z. No unique answer. Insufficient. (2) y = z Case 1: Say x is the smallest integer, then y or z is the median. The answer is Yes, z is the median of x, y, and z. Case 2: Say x is the largest integer, then y or z is the median. The answer is Yes, z is the median of x, y, and z. Case 3: Say x = y = z, then x, y or z is the median. The answer is Yes, z is the median of x, y, and z. Unique answer. Sufficient. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Manhattan Review Hyderabad | Dilsukhnagar GMAT Courses | Mehdipatnam GRE Prep | 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for 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 • FREE GMAT Exam Know how you'd score today for$0

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