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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 ## Seven cars of seven different models are going to park in tagged by: VJesus12 ##### This topic has 2 expert replies and 0 member replies ## Seven cars of seven different models are going to park in ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Seven cars of seven different models are going to park in a row of seven side-by-side parking spots for an advertisement. Model P and Model Q must park next to each other, and Model S must be somewhere to the right of Models P & Q. How many possible configurations are there for the cars? a) 600 b) 720 c) 1440 d) 4320 e) 4800 OA=B Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 VJesus12 wrote: Seven cars of seven different models are going to park in a row of seven side-by-side parking spots for an advertisement. Model P and Model Q must park next to each other, and Model S must be somewhere to the right of Models P & Q. How many possible configurations are there for the cars? a) 600 b) 720 c) 1440 d) 4320 e) 4800 Let the 7 cars be A, B, C, D, P, Q and S. Since P and Q must occupy adjacent positions, consider PQ a single element in the arrangement. The number of ways to arrange the 6 elements A, B, C, D, PQ and S = 6! = 720. In 1/2 of these arrangements, S will be to the LEFT of PQ. In the remaining 1/2 of these arrangements, S will be to the RIGHT of PQ. Thus, the number of arrangements in which S is to the right of PQ = (1/2)(720). Since PQ can switch to QP -- doubling the total number of possible arrangements -- we multiply by 2: (2)(1/2)(720) = 720. The correct answer is B. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 VJesus12 wrote: Seven cars of seven different models are going to park in a row of seven side-by-side parking spots for an advertisement. Model P and Model Q must park next to each other, and Model S must be somewhere to the right of Models P & Q. How many possible configurations are there for the cars? a) 600 b) 720 c) 1440 d) 4320 e) 4800 OA=B Source: Magoosh If models P and Q must park next to each other, we can consider them as one unit. That is, there are 6 cars (instead of 7) and they can be arranged in 6! = 720 ways. However, since P and Q are considered one unit, they can be arranged as either PQ or QP. Therefore, there are 720 x 2 = 1440 ways to arrange these cars if there are no other restrictions. However, we have a restriction that model S must be on the right of P and Q. Model S is to the right of P and Q in exactly half of the 1440 ways, and it is to the left of P and Q in the remaining half of the 1440 ways. Therefore, the number of ways S will be to the right of P and Q is Â½ x 1440 = 720. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Magoosh Study with Magoosh GMAT prep 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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