• NEW! FREE Beat The GMAT Quizzes  Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
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 ## OG Mixtures Problem ##### This topic has 6 expert replies and 2 member replies ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ? (A) 10% (B) 33 1/3% (C) 40% (D) 50% (E) 66 2/3% ### GMAT/MBA Expert GMAT Instructor Joined 11 Aug 2010 Posted: 511 messages Followed by: 86 members Upvotes: 344 aaggar7 wrote: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ? This can be treated as an weighted average problem where 30 is the weighted average of 25 and 40 and we need to find out the weight of 40 in the average. Say, the weight of 40 is x. Hence, weight of 25 is (1 - x) So, 40x + 25(1 - x) = 30 --> (40x - 25x) = (30 - 25) --> 15x = 5 --> x = 1/3 Required percentage = 100/3 = 33�" % The correct answer is B. _________________ Anju Agarwal Quant Expert, Gurome Backup Methods : General guide on plugging, estimation etc. Wavy Curve Method : Solving complex inequalities in a matter of seconds. § GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome § ### GMAT/MBA Expert GMAT Instructor Joined 11 Aug 2010 Posted: 511 messages Followed by: 86 members Upvotes: 344 Here is another different approach based on the same concept. In any weighted average, thee weight of any end point in the average will be (Difference between the other end-point and the weighted average)/(Difference between the two end-points) Hence, here weight of 40 in the average = |25 - 30|/|40 - 25| = 5/15 = 1/3 Required percentage = (1/3)*100 = 33�" The correct answer is B.[/quote] _________________ Anju Agarwal Quant Expert, Gurome Backup Methods : General guide on plugging, estimation etc. Wavy Curve Method : Solving complex inequalities in a matter of seconds. § GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome § Master | Next Rank: 500 Posts Joined 11 Mar 2012 Posted: 124 messages Followed by: 1 members Upvotes: 9 Thanks Anju ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15196 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 For a visual solution, check the second half of my post here: https://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. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10109 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight, seed mixture Y is 25 percent ryegrass and 75 percent fescue and a mixture of X and Y contains 30 percent ryegrass. We're asked for the percentage of the weight of the mixture that is seed X. This question can be solved in a couple of different ways, including by setting up a Weighted Average. X = number of pounds of seed mixture X Y = number of pounds of seed mixture Y Since we're mixing together a certain amount of X and Y - and the respective percentages of ryegrass are 40% and 25%, respectively - we can create the following equation: (.4X + .25Y)/(X+Y) = .3 .4X + .25Y = .3X + .3Y .1X = .05Y 10X = 5Y X/Y = 5/10 = 1/2 Thus, for every round of X, we have 2 pounds of Y and 3 pounds total. Thus, the percentage of the TOTAL mix that is seed mix X is 1/3 = 33 1/3% Final Answer: B GMAT assassins aren't born, they're made, Rich ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 829 messages Followed by: 4 members Let M = x + y M = new mixture x = Mixture X y = Mixture Y What do we need to find? (x/M)*100 Equating Ryegrass in the mixture, 0.4x + 0.25y = 0.3M 0.4x + 0.25(M-x) = 0.3M 0.4x + 0.25M - 0.25x = 0.3M 0.15x = 0.05M x/M = 1/3 Hence, B is the correct answer. Regards! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2244 messages Followed by: 17 members Upvotes: 43 aaggar7 wrote: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ? (A) 10% (B) 33 1/3% (C) 40% (D) 50% (E) 66 2/3% We are given information about ryegrass, bluegrass, and fescue. However, we are told the mixture of X and Y is 30 percent ryegrass. Thus, we care only about the ryegrass, so we can ignore fescue and bluegrass. We are given that seed mixture X is 40% ryegrass and that seed mixture Y is 25% ryegrass. We are also given that the weight of the combined mixture is 30% ryegrass. With x representing the total weight of mixture X, and y representing the total weight of mixture Y, we can create the following equation: 0.4x + 0.25y = 0.3(x + y) We can multiply the entire equation by 100: 40x + 25y = 30x + 30y 10x = 5y 2x = y The question asks what percentage of the weight of the mixture is x. We can create an expression for this: x/(x+y) * 100 = ? Since we know that 2x = y, we can substitute in 2x for y in our expression. So, we have: x/(x+2x) * 100 = x/(3x) * 100 = 1/3 * 100 = 33.33% Answer: B ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12740 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 aaggar7 wrote: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ? (A) 10% (B) 33 1/3% (C) 40% (D) 50% (E) 66 2/3% This looks like a job for weighted averages! Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Mixture X is 40 percent ryegrass Mixture Y is 25 percent ryegrass Let x = the PERCENT of mixture X needed (in other words, x/100 = the proportion of mixture X needed) So, 100-x = the PERCENT of mixture Y needed (in other words, (100-x)/100 = the proportion of mixture Y needed) Weighted average of groups combined = 30% Now take the above formula and plug in the values to get: 30 = (x/100)(40) + [(100-x)/100](25) Multiply both sides by 100 to get: 30 = 40x + (100-x)(25) Expand: 3000 = 40x + 2500 - 25x Simplify: 3000 = 15x + 2500 So: 500 = 15x Solve: x = 500/15 = 100/3 = 33 1/3 So, mixture X is 33 1/3 % of the COMBINED mix. Answer: B For more information on weighted averages, you can watch this video: http://www.gmatprepnow.com/module/gmat-statistics?id=805 Here are some additional practice questions related to weighted averages: - http://www.beatthegmat.com/weighted-averages-t117237.html - http://www.beatthegmat.com/weighted-average-t114506.html - http://www.beatthegmat.com/average-weight-of-men-and-women-t57853.html - http://www.beatthegmat.com/averages-question-t87118.html 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! • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

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

• 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 GMAT Exam
Know how you'd score today for \$0

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 Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

### Top First Responders*

1 GMATGuruNY 54 first replies
2 Brent@GMATPrepNow 41 first replies
3 Jay@ManhattanReview 40 first replies
4 Ian Stewart 30 first replies
5 ceilidh.erickson 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

197 posts
2 fskilnik@GMATH

GMATH Teacher

124 posts
3 Max@Math Revolution

Math Revolution

83 posts
4 GMATGuruNY

The Princeton Review Teacher

81 posts
5 Brent@GMATPrepNow

GMAT Prep Now Teacher

66 posts
See More Top Beat The GMAT Experts