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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 scientist has 400 units of a 6% phosphoric acid solution, tagged by: swerve ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A scientist has 400 units of a 6% phosphoric acid solution, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution? A. 200 B. 400 C. 500 D. 600 E. 800 The OA is E Source: Magoosh ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10071 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, While an Algebra approach (using the "weighted average" formula) would work nicely on this prompt, you can also answer it rather quickly by TESTing THE ANSWERS and using a bit of logic. Here, we're going to mix 400 ounces of a 6% acid solution with X ounces of a 12% acid solution to form a 10% acid solution. We're asked for the value of X. The answers are all nice, round numbers, so we can take advantage of them.... Let's start with Answer B.... IF..... X = 400 ounces Then we'd have the same amount of each solution: 400 ounces of 6% and 400 ounces of 12% --> this would produce a (6%+12%)/2 = 9% mixture This is TOO SMALL. X must be BIGGER. Eliminate Answers A and B. Now, let's TEST Answer D... IF.... X = 600 ounces Then with 400 ounces of 6% and 600 ounces of 12%, we'd have... [(400)(.06) + (600)(.12)]/(400 + 600) = (24 + 72)/1000 = 96/1000 = 9.6%, This is also TOO SMALL. X must be BIGGER. Eliminate C and D. Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2012 messages Followed by: 14 members Upvotes: 43 swerve wrote: A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution? A. 200 B. 400 C. 500 D. 600 E. 800 The OA is E Source: Magoosh We will add 400 units of 6% solution to x units of 12% solution to obtain a total of (400 + x) units of 10% solution. We can create the following equation: 0.06(400) + 0.12x = 0.1(400 + x) 24 + 0.12x = 40 + 0.1x 0.02x = 16 x = 16/0.02 = 800 Answer: E _________________ Scott Woodbury-Stewart Founder and CEO ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12655 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 swerve wrote: A scientist has 400 units of a 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce a 10% phosphoric acid solution? A. 200 B. 400 C. 500 D. 600 E. 800 The OA is E Source: Magoosh We can solve this question with the weighted averages formula: Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let x = the number of units of 12% phosphoric acid solution needed Since we're adding x units to 400 units, the volume of the RESULTING mixture = 400 + X A scientist has 400 units of a 6% phosphoric acid solution. . . So, the PROPORTION of 6% solution in the RESULTING mixture = 400/(400 + x) . . . and an unlimited supply of 12% phosphoric acid solution We are adding x units of 12% solution So, the PROPORTION of 12% solution in the RESULTING mixture = x/(400 + x) How many units of the latter must she add to the former to produce a 10% phosphoric acid solution? We want the resulting mixture to contain 10% phosphoric acid Applying the formula, we can write: 10 = [400/(400 + x)][6] + [x/(400 + x)][12] Multiply both sides by (400 + x) to get: 10(400 + x) = 2400 + 12x Expand left side to get: 4000 + 10x = 2400 + 12x Solve: x = 800 Answer: E Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Award-winning private GMAT tutoring Register now and save up to$200

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