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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 ## Ratio and Proportion OG 12ed #66 ##### This topic has 3 expert replies and 2 member replies ## Ratio and Proportion OG 12ed #66 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the number of first graders to the number of third graders? a) 16 to 15 b) 9 to 5 c) 5 to 16 d) 5 to 4 e) 4 to 5 Is there a better explanation than the one provided in the OG? ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14806 messages Followed by: 1850 members Upvotes: 13060 GMAT Score: 790 Quote: At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. if the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the ratio of the number of first graders to the number of third graders? A. 16 to 15 B. 9 to 5 C. 5 to 16 D. 5 to 4 E. 4 to 5 A very fast approach: 1st/3rd = 1st/2nd * 2nd/4th * 4th/3rd. In the equation above, all of the values in red cancel out. Thus: 1st/3rd = 3/4 * 8/5 * 2/3 = 4/5. The correct answer is E. _________________ 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. Master | Next Rank: 500 Posts Joined 23 Jun 2013 Posted: 283 messages Followed by: 25 members Upvotes: 97 Test Date: August 12, 2013 GMAT Score: 750 juliet.foster@gmail.com wrote: At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the number of first graders to the number of third graders? a) 16 to 15 b) 9 to 5 c) 5 to 16 d) 5 to 4 e) 4 to 5 Is there a better explanation than the one provided in the OG? Number of first graders = A Number of second graders = B Number of third graders = C Number of fourth graders = D B/D = 8/5 A/B = 3/4 C/D = 3/2 A/C = ? We need to find A in terms of C A = (3/4)B A = (3/4)(8/5)D A = (3/4)(8/5)(2/3)C A = (4/5)C A/C = 4/5 Choose e Cheers _________________ Every job is a self-portrait of the person who did it. Autograph your work with excellence. Kelley School of Business (Class of 2016) GMAT Score: 750 V40 Q51 AWA 5 IR 8 https://www.beatthegmat.com/first-attempt-750-in-2-months-t268332.html#688494 Master | Next Rank: 500 Posts Joined 08 Nov 2013 Posted: 447 messages Followed by: 1 members Upvotes: 25 Originally I tried working out lowest common multiples, so that the fractions would all disappear, but the excess of arithmetic seemed redundant. List given ratios in order (this just makes the question easier to read) 1st:2nd = 3:4 2nd:4th = 8:5 3rd:4th = 3:2 Work out the required "ratio journey" [1st -> third] = [1st -> 2nd -> 4th -> 3rd] = 3:4 -> 8:5 -> 2:3 (in the form x:y) The product of x values, X = 3 x 8 x 2 = 48 The product of y values, Y = 4 x 5 x 3 = 60 So the overall ratio (X,Y) = 48:60 = 4:5 No different to the 2 previous solutions really, except for the presentation of the algorithm. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 9832 messages Followed by: 490 members Upvotes: 2867 GMAT Score: 800 Hi juliet.foster, In these types of ratio questions, you can TEST VALUES; you just have to make sure that you test numbers that match the given information. We have 1st, 2nd, 3rd and 4th graders. Based on the given ratios, we know the that the number of 4th graders has to be a multiple of 2 AND a multiple of 5. Let's pick: 4th graders = 10 Based on the given ratios, we'd haveâ€¦. 3rd graders = 15 2nd graders = 16 1st graders = 12 The ratio of 1st to 3rd graders is: 12:15 This reduces to: 4:5 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 09 Apr 2015 Posted: 1461 messages Followed by: 16 members Upvotes: 39 juliet.foster@gmail.com wrote: At a certain school, the ratio of the number of second graders to the number of fourth graders is 8 to 5, and the ratio of the number of first graders to the number of second graders is 3 to 4. If the ratio of the number of third graders to the number of fourth graders is 3 to 2, what is the number of first graders to the number of third graders? a) 16 to 15 b) 9 to 5 c) 5 to 16 d) 5 to 4 e) 4 to 5 Is there a better explanation than the one provided in the OG? Solution: Background: Ratios show the relationship between members of two or more categories. As an example, if the ratio of horses to ponies is 7:4 and the ratio of ponies to goats is 4:2, then we can directly express the ratio of horses to goats as 7:2 because the original ratios had matching values for ponies. A more complicated pair of ratios would be horses to ponies is 7:4 and ponies to goats is 2:1. We must make the ponies numbers equal in both ratios before being able to directly express the ratio of horses to goats. We would thus multiply the second ratio (ponies to goats) by 2 to get the equivalent ratio of 4:2. Now that the ponies numbers match, we can directly express the ratio of horses to goats as 7:2. We are given the following: 1) The ratio of the number of second graders to the number of fourth graders is 8 to 5. 2) The ratio of the number of first graders to the number of second graders is 3 to 4. 3) The ratio of the number of third graders to the number of fourth graders is 3 to 2. That is: 1) 2nd : 4th = 8 : 5 2) 1st : 2nd = 3 : 4 3) 3rd : 4th = 3 : 2 From the first and second ratios, we see that they both contain 2nd graders, so letâ€™s make 2nd graders the same number. We see that the number for 2nd graders in the first ratio is 8 and that for the 2nd graders in the second ratio is 4. We multiply the second ratio by 2, obtaining 6 : 8, and now both ratios have a matching 8 for 2nd graders. 1) 2nd : 4th = 8 : 5 2) 1st : 2nd = 6 : 8 Now we see that the ratio of 4th graders to 1st graders must be 5 to 6. That is: 4th : 1st = 5 : 6 We will now compare this with the third ratio we set up originally: 3rd : 4th = 3 : 2 We see that both ratios contain 4th graders, so letâ€™s make 4th graders the same number. We must change both ratios. We multiply the ratio 5 : 6 by 2, to get an equivalent ratio of 10 : 12. Then we multiply the ratio 3 : 2 by 5, to get an equivalent ratio of 15 : 10. That is: 4th : 1st = 10 : 12 3rd : 4th = 15 : 10 Now that 4th graders have a matching 10 in each ratio, we can express the ratio of 1st graders to 3rd graders as 12 : 15. That is: 1st : 3rd = 12 : 15 We can reduce this ratio by dividing both 12 and 15 by 3: 1st : 3rd = 4 : 5 Answer: E _________________ Jeffrey Miller Head of GMAT Instruction • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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