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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 ## In a group of children, the average (arithmetic mean) weight tagged by: swerve ##### This topic has 3 expert replies and 0 member replies ### Top Member ## In a group of children, the average (arithmetic mean) weight ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, and the average weight of the girls is 48 pounds. If the average weight of all of the children in the group is 50 pounds, what is the ratio of the number of boys to the number of girls? A. 1/12 B. 1/6 C. 1/5 D. 1/4 E. 1/3 The OA is C Source: Magoosh ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that in a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, the average weight of the girls is 48 pounds and the average weight of ALL of the children in the group is 50 pounds. We're asked for the ratio of the number of boys to the number of girls. This question can be solved in a number of different ways, including by TESTing THE ANSWERS. There's an interesting Number Property pattern that you can also take advantage of though (that can save you a bit of work REGARDLESS of which approach you use). To start, since the average weight of ALL the children is 50 pounds, we know that the TOTAL weight of the children is a MULTIPLE OF 50... and that total ends in a '0.' Since the average weight of the boys is 60 pounds, we know that that sum will end in a '0.' The average weight of the girls is 48 pounds though, so will also need the total weight of this group to also be a multiple of 10... otherwise the sum of ALL the children won't end in a '0.' The only ways for that to occur are when the total number of girls is a MULTIPLE OF 5.... Looking at the answer choices, there's only one answer that fits... but here's how you can prove it's the correct answer by TESTing THE ANSWERS: IF we have 1 boy and 5 girls... then the total weight is 1(60) + 5(48) = 60 + 240 = 300 and the average weight is 300/6 = 50 pounds. This fits what we were told, so the ratio MUST be 1:5 = 1/5 Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12985 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 swerve wrote: In a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, and the average weight of the girls is 48 pounds. If the average weight of all of the children in the group is 50 pounds, what is the ratio of the number of boys to the number of girls? A. 1/12 B. 1/6 C. 1/5 D. 1/4 E. 1/3 We can also use weighted averages to solve this Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let G = number of girls Let B = number of boys So, G+B = TOTAL number of children And G/(G+B) = proportion of girls in the group And B/(G+B) = proportion of boys in the group Plug all values into formula to get: 50 = [B/(G+B)][60] + [G/(G+B)][48] Rewrite to get: 50 = 60B/(G+B) + 48G/(G+B) Multiply both sides by (G+B) to get: 50(G+B) = 60B + 48G Expand left side to get: 50G + 50B = 60B + 48G Subtract 48G from both sides to get: 2G + 50B = 60B Subtract 50B from both sides to get: 2G = 10B Divide both sides by 10 to get: 2G/10 = B Divide both sides by G to get: 2/10 = B/G Simplify: 1/5 = B/G So, the ratio of boys to girls = B/G = 1/5 Answer: C 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 â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these 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 GMAT Instructor Joined 25 Apr 2015 Posted: 2801 messages Followed by: 18 members Upvotes: 43 swerve wrote: In a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, and the average weight of the girls is 48 pounds. If the average weight of all of the children in the group is 50 pounds, what is the ratio of the number of boys to the number of girls? A. 1/12 B. 1/6 C. 1/5 D. 1/4 E. 1/3 The OA is C Source: Magoosh Letting b and g equal the number of boys and girls, respectively, we can create the weighted average equation: (60b + 48g)/(b + g) = 50 60b + 48g = 50b + 50g 10b = 2g 5b = g b/g = 1/5 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 • Award-winning private GMAT tutoring Register now and save up to$200

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