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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 the perimeter of triangle ABC greater than 12 cm? tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## Is the perimeter of triangle ABC greater than 12 cm? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult e-GMAT Is the perimeter of triangle ABC greater than 12 cm? 1) One side of triangle ABC measures 6 cm. 2) The lengths of the three sides of triangle ABC are consecutive positive even integers. OA D ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 AAPL wrote: e-GMAT Is the perimeter of triangle ABC greater than 12 cm? 1) One side of triangle ABC measures 6 cm. 2) The lengths of the three sides of triangle ABC are consecutive positive even integers. All lengths are measured in centimeters. $$a + b + c\,\,\mathop > \limits^? \,\,12$$ $$\left( 1 \right)\,\,{\rm{WLOG}}\,\left( * \right)\,\,\,a = 6\,\,\,\,\,\mathop \Rightarrow \limits^{\Delta \,\,{\rm{exists!}}} \,\,\,\,6 = a < b + c\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,$$ (*) WLOG = without loss of generality \eqalign{ & \left( 2 \right)\,\,a + b + c = 2M + 2M + 2 + 2M + 4 = 6M + 6\,\,,\,\,\,M \ge 2\,\,{\mathop{\rm int}} \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \cr & \left( {M = 1\,\,\, \Rightarrow \,\,\,\,2,4,6\,\,{\rm{is}}\,\,{\rm{not}}\,\,{\rm{a}}\,\,{\rm{triangle!}}} \right) \cr} (We have NOT said that a, b and c are respectively equal to 2M, 2M+2 and 2M+4 ... be careful!) 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: 1979 messages Followed by: 30 members Upvotes: 470 AAPL wrote: e-GMAT Is the perimeter of triangle ABC greater than 12 cm? 1) One side of triangle ABC measures 6 cm. 2) The lengths of the three sides of triangle ABC are consecutive positive even integers. OA D Say the three sides are a, b and c. Thus, perimeter = a + b + c. We have to ascertain whether a + b + c > 12. Let's take each statement one by one. 1) One side of triangle ABC measures 6 cm. Note that the sum of any two sides is greater than the third side. Say a = 6, thus, b + c > 6 => a + b + c > 12. Sufficient. 2) The lengths of the three sides of triangle ABC are consecutive positive even integers. Case 1: Say the three sides are 2, 4, and 6, minimum possible consecutive positive even integers. However, this combination of sides will not render a triangle since the sum of the smaller sides = 2 + 4 = 6 is not greater than the third side ( = 6). Case 2: Say the three sides are 4, 6, and 8, next possible consecutive positive even integers. This combination of the sides renders a triangle since the sum of the smaller sides = 4 + 6 = 10 > third side (= 8). Perimeter = 4 + 6 + 8 = 18 > 12. Sufficient. There is no need to check other cases such as 6, 8 and 10; 8, 10, and 12, etc. since they all form triangles and perimeter > 12. Sufficient. The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review New Delhi | Hyderabad | GRE Prep Chennai | Madhapur GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for0

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