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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 ## The participants in a race consisted of 3 teams with 3 ##### This topic has 2 expert replies and 0 member replies ### Top Member ## The participants in a race consisted of 3 teams with 3 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 -n points if one of its runners finished in nth place, where 1 <= n <= 5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point? (1) No team was awarded more than a total of 6 points. (2) No pair of teammates finished in consecutive places among the top five places. OA A Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 870 messages Followed by: 27 members Upvotes: 59 BTGmoderatorDC wrote: The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 -n points if one of its runners finished in nth place, where 1 <= n <= 5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point? (1) No team was awarded more than a total of 6 points. (2) No pair of teammates finished in consecutive places among the top five places. Source: Princeton Review $A,B,C\,\,{\text{teams}}\,\,\left( {3\,\,{\text{people}}\,\,{\text{in}}\,\,{\text{each}}} \right)$ $?\,\,:\,\,{\text{all}}\,\,{\text{teams}}\,\,{\text{got}}\,\,{\text{points}}$ $\begin{array}{*{20}{l}} {{\text{Place}}}&{{\text{Points}}} \\ 1&5 \\ 2&4 \\ 3&3 \\ 4&2 \\ 5&1 \end{array}$ $15\,\,{\text{points}}\,\,{\text{given}}\,\,{\text{in}}\,\,{\text{total}}\,\,\,\left( * \right)$ $\left( 1 \right)\,\sum {{\text{any}}\,{\text{two}}\,\,{\text{teams}}} \,\,\, \leqslant \,\,12\,\,{\text{points}}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$ $\left( 2 \right)\,\,\,\left\{ \begin{gathered} \hfill \,{\text{Take}}\,\,A = \left\{ {1,3,5} \right\}\,\,{\text{and}}\,\,B = \left\{ {2,4} \right\}\,\,\,\left( {{\text{places}}} \right)\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \\ \hfill \,{\text{Take}}\,\,A = \left\{ {1,3} \right\}\,,\,B = \left\{ {2,4} \right\}\,\,{\text{and}}\,\,C = \left\{ 5 \right\}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \\ \end{gathered} \right.$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version) Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1531 messages Followed by: 27 members Upvotes: 470 BTGmoderatorDC wrote: The participants in a race consisted of 3 teams with 3 runners on each team. A team was awarded 6 -n points if one of its runners finished in nth place, where 1 <= n <= 5. If all of the runners finished the race and if there were no ties, was each team awarded at least one point? (1) No team was awarded more than a total of 6 points. (2) No pair of teammates finished in consecutive places among the top five places. OA A Source: Princeton Review Given there are 6 teams with 3 3 runners on each team, we have 3*3 = 9 runners. Again given, the points awarded equal to 6 - n, where n = position of the runner in the race; and 1 â‰¤ n â‰¥ 5, only the first five positions will be awarded points. We know that all of the runners finished the race and there were no ties. Question: Was each team awarded at least one point? Say the three runners of the teams are represented by T1, T2, and T3. Let's take each statement one by one. (1) No team was awarded more than a total of 6 points. In order to test the question, we must think of a scenario such that none of the runners of a team wins. So, all the five positions must be won by the other two teams. The number of points accrued by winning all five positions equals to 5 + 4 + 3 + 2 + 1 = 15. However, as per Statement 1, the maximum points a team can earn is 6, thus, the maximum points two teams can earn is 6 + 6 = 12. Thus, the third team must have earned at least 15 - 12 = 3 points. The answer is yes, each team was awarded at least one point. Sufficient. (2) No pair of teammates finished in consecutive places among the top five places. Say the first five positions are lined up as given below. Case 1: T1, T2, T1, T2, T1. T3 team runners come after 5th position, earning them no points. The answer is no, each team was NOT awarded at least one point. Case 2: T1, T2, T1, T2, T3. A T3 team runner comes at 5th position, earning it 1 point. The answer is yes, each team was awarded at least one point. No unique answer. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Manhattan Review Hyderabad | Madhapur GMAT Courses | Dilsukhnagar GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! 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