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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 ## You have access to an unlimited number of each of the follow tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## You have access to an unlimited number of each of the follow ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 3) You have access to an unlimited number of each of the following coins: pennies, nickels, dimes and quarters. Which of the following amounts CAN be made using exactly 6 of these coins? I. 76 cents II. 81 cents III. 29 cents IV. 101 cents (A) None of them (B) Exactly one of them (C) Exactly two of them (D) Exactly three of them (E) All of them Answer: ____(C)__ _________________ 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 3) You have access to an unlimited number of each of the following coins: pennies, nickels, dimes and quarters. Which of the following amounts CAN be made using exactly 6 of these coins? I. 76 cents II. 81 cents III. 29 cents IV. 101 cents (A) None of them (B) Exactly one of them (C) Exactly two of them (D) Exactly three of them (E) All of them $$?\,\,\,:\,\,\,{\rm{possible}}\,\,{\rm{amounts}}\,\,\,\,\left( {{\rm{with}}\,\,6\,\,{\rm{coins}}} \right)$$ $${\rm{I}}.\,\,\,76 = 1 \cdot 1 + 3 \cdot 25 = 1 \cdot 1 + 2 \cdot 25 + 2 \cdot 10 + 1 \cdot 5\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,1\,{\rm{nickel}}\,,\,\,2\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}$$ $${\rm{II}}.\,\,81 = 76 + 5 = 1 \cdot 1 + 2 \cdot 25 + 3 \cdot 10\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny}}\,,\,\,3\,\,{\rm{dimes}}\,,\,\,2\,\,{\rm{quarters}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{possible!}}$$ $${\rm{III}}{\rm{.}}\,\,29\,\,\, \Rightarrow \,\,\,\,4\,{\rm{pennies}}\,\,{\rm{ ARE}}\,\,\,\,{\rm{needed}} \ldots \,\,{\rm{exactly}}\,\,{\rm{2}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,25{\rm{?}}\,\,\,{\rm{impossible}}!$$ $${\rm{IV}}{\rm{.}}\,\,{\rm{101}}\,\,\,\, \Rightarrow \,\,\,\,1\,{\rm{penny IS}}\,\,{\rm{needed}} \ldots \,\,{\rm{5}}\,\,{\rm{coins}}\,\,{\rm{for}}\,\,{\rm{100?}}\,\,\,\left\{ \matrix{ \,4 \cdot 25\,\,{\rm{impossible}}\,\,\left( {{\rm{only}}\,\,5\,\,{\rm{coins}}\,\,{\rm{in}}\,\,{\rm{total}}} \right) \hfill \cr \,3 \cdot 25\,\,{\rm{impossible}}\,\,\left( {2\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,25?} \right) \hfill \cr \,2 \cdot 25\,\,{\rm{impossible }}\left( {3\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,50?} \right) \hfill \cr \,1 \cdot 25\,\,{\rm{impossible }}\left( {4\,\,{\rm{not - quarters}}\,\,{\rm{adding}}\,\,75?} \right)\, \hfill \cr} \right.$$ The correct answer is (C). 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 Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 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 • Award-winning private GMAT tutoring Register now and save up to$200

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