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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 ## Little Julia created a 5-digit integer choosing 5 distinct c tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## Little Julia created a 5-digit integer choosing 5 distinct c ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 18) Little Julia created a 5-digit integer choosing 5 distinct chips, one by one, among the 7 given ones shown above. "Can you do it in such a way that the three central digits add up to 9?", asked her teacher. And Julia did! If little Max was asked to do the same by his teacher, and Max chooses a correct possibility randomly, what is the probability that both children have chosen exactly the same 5-digit integer? (A) 1/12 (B) 1/36 (C) 1/54 (D) 1/72 (E) 1/96 Answer: _____(D)__ _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 18) Little Julia created a 5-digit integer choosing 5 distinct chips, one by one, among the 7 given ones shown above. "Can you do it in such a way that the three central digits add up to 9?", asked her teacher. And Julia did! If little Max was asked to do the same by his teacher, and Max chooses a correct possibility randomly, what is the probability that both children have chosen exactly the same 5-digit integer? (A) 1/12 (B) 1/36 (C) 1/54 (D) 1/72 (E) 1/96 $$?\,\, = \,\,{1 \over {\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}}}$$ $${?_{temp}}\,\,\, = \,\,\,\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}$$ $$\left\{ \matrix{ \,{\rm{3}}\,{\rm{central}}\,{\rm{digits}}\,{\rm{are}}\,\,{\rm{1,3,5}}\,\,\,\, \Rightarrow \,\,\,{{\rm{P}}_{\rm{3}}} = 3!\,\,\,{\rm{possibilities}} \hfill \cr \,{\rm{first}}\,{\rm{and}}\,\,{\rm{last}}\,\,{\rm{digits}}\,\,\,{\rm{:}}\,\,\,{\rm{4}} \cdot {\rm{3}}\,\,{\rm{possibilities}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{?_{temp}}\,\,\, = \,\,\,3!\, \cdot 4 \cdot 3\,\, = \,\,\,72$$ The correct answer is (D). We follow 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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