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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 ## Solution Y is 40 percent sugar by volume, and solution X... tagged by: Brent@GMATPrepNow ##### This topic has 4 expert replies and 0 member replies ### Top Member ## Solution Y is 40 percent sugar by volume, and solution X... Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. how many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume? (A) 37.5 (B) 75 (C) 150 (D) 240 (E) 450 The OA is E. Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12534 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 chaitanya.bhansali wrote: Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume? A) 37.5 B) 50 C) 62.5 D) 300 E) 450 When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED. Start with 150 gallons of solution that is 40% sugar: When we draw this with the ingredients separated, we see we have 60 gallons of sugar in the mixture. Next, we'll let x = the number of gallons of solution X we need to add. Since 20% of the solution X is sugar, we know that 0.2x = the volume of sugar in this solution: At this point, we can ADD the two solutions (PART BY PART) to get the following volumes: Since the resulting solution is 25% sugar (i.e., 25/100 of the solution is sugar), we can write the following equation: (60 + 0.2x)/(150 + x) = 25/100 Simplify to get: (60 + 0.2x)/(150 + x) = 1/4 Cross multiply to get: 4(60 + 0.2x) = 1(150 + x) Expand: 240 + 0.8x = 150 + x Rearrange: 90 = 0.2x Solve: x = 450 Answer: E Cheers, Brent Here are some additional mixture questions to practice with: http://www.beatthegmat.com/liters-of-mixture-x-in-the-50-mixture-t271387.html http://www.beatthegmat.com/percentage-mixture-t268631.html http://www.beatthegmat.com/rodrick-mixes-a-martini-that-has-a-volume-of-n-ounces-havi-t270387.html http://www.beatthegmat.com/mixure-problem-quite-confusing-t261767.html http://www.beatthegmat.com/mixture-ratio-problem-2-t191643.html _________________ Brent Hanneson â€“ 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 GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10014 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi swerve, We're told that Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. We're asked for the number of gallons of Solution X that must be added to 150 gallons of Solution Y to create a solution that is 25 percent sugar by volume. This prompt is an example of a Weighted Average question - and while you can certainly solve it Algebraically, you can also TEST THE ANSWERS. To start, IF we had an EQUAL amount of both Solutions in the mixture, then the average sugar percent would be (40+20)/2 = 30. That's not what we're after though - we want there to be a 25% average, so we clearly need MORE of Solution X than Solution. Y. We're told that there is 150 gallons of Solution Y in the mixture, so there has to be MORE than 150 gallons of Solution X. Thus, we can eliminate Answers A, B and C. Let's TEST Answer E: 450 gallons IF we have.... 150 gallons of Solution Y and 450 gallons of Solution X, the ratio of Y:X is 1:3 and the average sugar content would be... [(1)(40) + (3)(20)]/(1+3) = [40 + 60]/4 = 100/4 = 25 percent This matches what we were told, so this MUST be the answer. 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 12 Sep 2012 Posted: 2636 messages Followed by: 114 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 If we've got 150 gallons of solution Y, then 40% of 150, or 60 gallons of it are sugar. From here, we're adding x gallons of Solution X. 20% of that is sugar, so sugar / total = (60 + 0.2x) / (150 + x) is our ratio. We need that to equal 25%, or 1/4, so (60 + 0.2x) / (150 + x) = 1/4 Then just cross multiply and solve for x: 4 * (60 + 0.2x) = 150 + x 240 + 0.8x = 150 + x 90 = 0.2x 450 = x Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 12 Sep 2012 Posted: 2636 messages Followed by: 114 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Another approach would be finding the weighted average. If X is 20% sugar, Y is 40% sugar, and X + Y = 25% sugar, then .2x + .4y = .25(x + y) .2x + .4y = .25x + .25y .15y = .05x 3y = x We were told y = 150, so x = 3y = 3*150 = 450. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. 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