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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 ## A dessert recipe calls for 50% melted chocolate and 50% ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A dessert recipe calls for 50% melted chocolate and 50% ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each? A. 1.5 B. 2.5 C. 3 D. 4.5 E. 5 OA B Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each? A. 1.5 B. 2.5 C. 3 D. 4.5 E. 5 Source: Veritas Prep $$?\,\,\, = \,\,\,x = \# \,\,{\text{out}}\,\,\underline {{\text{sauce}}} \,\,{\text{cups}}\,\, = \,\,\# \,\,{\text{in}}\,\,\underline {{\text{100 % }}\,\,{\text{choco}}} \,\,{\text{cups}}$$ $$\matrix{ {{\rm{real}} \to {\rm{ideal}}} \cr {15\,\,{\rm{cups}}} \cr } \,\,\,\left\{ \matrix{ \,{\rm{choco}}\,:\,\,{2 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {2 \over 5}\,\,{\rm{cups}} + x\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,{\rm{cups}} \hfill \cr \,{\rm{rasp}}\,:\,\,{3 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {3 \over 5}\,\,{\rm{cups}} + 0\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,{\rm{cups}} \hfill \cr} \right.$$ $${3 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {3 \over 5}\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{3 \over 5}x = {{0.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 2.5$$ $$\left[ {\,{2 \over 5}\left( {15} \right)\,\,{\rm{cups}} - x \cdot {2 \over 5}\,\,{\rm{cups}} + x\,\,{\rm{cups}}\,\,\,\,\, = \,\,\,\,{{2.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{3 \over 5}x = {{0.5} \over 5}\left( {15} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x = 2.5} \right]$$ The correct answer is (B). 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 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15344 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply BTGmoderatorDC wrote: A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 40% melted chocolate and 60% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each? A. 1.5 B. 2.5 C. 3 D. 4.5 E. 5 Chocolate percentage in the incorrect sauce: 40%. Chocolate percentage in the pure chocolate: 100%. Chocolate percentage in the mixture: 50%. Let I = the incorrect sauce and C = the pure chocolate. The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. Step 1: Plot the 3 percentages on a number line, with the percentages for I and C on the ends and the percentage for the mixture in the middle. I 40%----------50%-----------100% C Step 2: Calculate the distances between the percentages. I 40%----10----50%----50-----100% C Step 3: Determine the ratio in the mixture. The ratio of I to C is equal to the RECIPROCAL of the distances in red. I:C = 50:10 = 5:1. Since I:C = (5 cups) : (1 cup), 1 of every 6 cups must be pure chocolate. Thus: Pure chocolate = (1/6)(15 cups) = 15/6 = 5/2 = 2.5 cups. The correct answer is B. For two similar problems, check here: http://www.beatthegmat.com/ratios-fraction-problem-t115365.html _________________ 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. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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