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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 solution consists of only water and alcohol such that the tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## A solution consists of only water and alcohol such that the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult e-GMAT A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol? 1. Total quantity of the resulting solution is 350 milliliters. 2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water. OA A. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 AAPL wrote: e-GMAT A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol? 1. Total quantity of the resulting solution is 350 milliliters. 2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water. In the solution below, the unit considered is always milliliters. LetÂ´s use the k technique, one of the best tools of our method when dealing with ratios/proportions! $$\left\{ \matrix{ \,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k \hfill \cr \,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k + x \hfill \cr \,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,\,\,\,{{7k} \over {10k + x}} = {3 \over 5}\,\,\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{{\rm{cross - multiply}}} \,\,\,\,\,\,5k = 3x\,\,\,\,\,\left( * \right)$$ $$? = x$$ $$\left( 1 \right)\,\,\,10k + x = 350\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,6x + x = 350\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\,$$ $$\left( 2 \right)\,\,{a \over w} = {{10.5} \over {4.5}}\,\,\left( { = {{105} \over {45}} = {7 \over 3}} \right)\,\,\,{\rm{already}}\,\,{\rm{known}}\,\,{\rm{pre - statements}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\,\,\,$$ This solution follows 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 Apr 2015 Posted: 2456 messages Followed by: 18 members Upvotes: 43 AAPL wrote: e-GMAT A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in milliliters) so that the resulting solution contains 60% alcohol? 1. Total quantity of the resulting solution is 350 milliliters. 2. The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water. We can let the amount of water to be added be w and the original amount of alcohol and water be 7x and 3x, respectively. We can create the equation: (3x + w)/(7x + 3x + w) = 6/10 (3x + w)/(10x + w) = 3/5 5(3x + w) = 3(10x + w) 15x + 5w = 30x + 3w 2w = 15x We need to determine the value of w. We see that w = 15x/2 or x = 2w/15. Therefore, if we know one of the two variables, then we know the other. Statement One Only: Total quantity of the resulting solution is 350 milliliters. This means 10x + w = 350. Since x = 2w/15, we have: 10(2w/15) + w = 350 4w/3 + w = 350 4w + 3w = 1050 7w = 1050 w = 150 Statement one alone is sufficient. Statement Two Only: The original solution contains 10.5 milliliters of alcohol for every 4.5 milliliters of water. This means original amount of alcohol and water are 10.5y and 4.5y, respectively. Therefore, we have: 7x = 10.5y and 3x = 4.5y Either way, we have x = 1.5y. However, since y can be any positive number (for example, if y = 2, then x = 3 and if y = 4, then x = 6), we canâ€™t determine a unique value of x, and therefore, we canâ€™t determine the value of w. Statement two alone is not sufficient. Answer: A _________________ 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 • Award-winning private GMAT tutoring Register now and save up to$200

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