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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 ## Mixture problem tagged by: Mo2men ##### This topic has 3 expert replies and 0 member replies ## Mixture problem ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A vessel of capacity 2 liter has 25% of alcohol and another vessel of capacity 6 liter had 40% alcohol. Both liquids were poured out in one vessel.. What is approximately the new concentration of Mixture? A) 20% B) 30% C) 37.5% D) 50% E) 66.67% OA: C Dear GMAT Guru Can you please show the alligation method here? Thanks ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Top Reply Mo2men wrote: A vessel of capacity 2 liter has 25% of alcohol and another vessel of capacity 6 liter had 40% alcohol. Both liquids were poured out in one vessel.. What is approximately the new concentration of Mixture? A) 20% B) 30% C) 37.5% D) 50% E) 66.67% OA: C Dear GMAT Guru Can you please show the alligation method here? Thanks 2 liters of 25% solution are combined with 6 liters of 40% solution. Average percentage for the entire 8 liters = (2*25 + 6*40)/8 = 290/8 = 36.25. The closest answer is C. Alligation approach: Let V1 and V2 = the two vessels and M = the mixture. Step 1: Plot the three percents on a number line, with the percents for V1 and V2 on the ends and M in the middle. V1 25-----------M-----------40 V2 Step 2: Calculate the distances between V1, M and V2. This distances on the number of line are determined by the RECIPROCAL of the following ratio: (volume of V1)/(volume of V2). = 2/6 = 1/3 = x/3x Plotting the reciprocal of this ratio on the number line, we get: V1 25----3x----M----x----40 V2 Step 3: Determine the value of x. The number line indicates that the total distance (3x+x) is equal to the difference between 40 and 25: 3x+x = 40-25 4x = 15 x = 15/4 = 3.75 Since the percentage for M is x less than the percentage for V2, we get: M = V2-x = 40-3.75 = 36.25 The closest answer is C. _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2531 messages Followed by: 353 members Upvotes: 1090 GMAT Score: 780 The answer needs to be between 25% and 40%, and because we're using more of the 40% solution, the answer must be closer to 40%, so only one answer makes sense, 37.5%. That's assuming both vessels are full, something the question needs to mention (but doesn't). If you want to use alligation, you can draw a number line with the percentages for each component, and the overall percentage A in the middle: ---25-------d---------A---e--40---- Because the parts are in a 6 to 2, or 3 to 1 ratio, the distances I've labeled d and e are in a 3 to 1 ratio. So d is 3/4 of the total distance between 25 and 40, so is (3/4)(15) = 45/4 = 11.25, and A = 36.25. I suppose that's "approximately" 37.5, but that's a very bizarre "correct" answer to this question when a number like 36 is a much better approximation. What is the source? _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Mo2men wrote: A vessel of capacity 2 liter has 25% of alcohol and another vessel of capacity 6 liter had 40% alcohol. Both liquids were poured out in one vessel.. What is approximately the new concentration of Mixture? A) 20% B) 30% C) 37.5% D) 50% E) 66.67% OA: C (2 x 0.25 + 6 x 0.4)/(2 + 6) = (0.5 + 2.4)/8 = 2.9/8 â‰ˆ 3/8 = 0.375 = 37.5% Alternate Solution: We start with 2 liters of 25% alcohol and add to it 6 liters of 40% solution, and the result is 8 liters of x% solution. Letâ€™s express this information as an equation: 2(0.25) + 6(0.40) = 8(x) 0.5 +2.4 = 8x 5 + 24 = 80x 29/80 = x We can approximate this answer with 30/80 = â…œ which is about 37.5% Answer: C _________________ 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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