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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 ## 1/4 of all the juniors and 2/3 of all the seniors are... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## 1/4 of all the juniors and 2/3 of all the seniors are... 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip? (A) 4/9 (B) 1/2 (C) 2/3 (D) 1/3 (E) 5/6 The OA is B. I can understand this PS question. Can any expert explain it please? Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 LUANDATO wrote: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip? (A) 4/9 (B) 1/2 (C) 2/3 (D) 1/3 (E) 5/6 Let the total number of seniors = the LCM of the denominators in the prompt = 4*3 = 12. Since there are 2/3 as many juniors as seniors, the total number of juniors = (2/3)(12) = 8. Thus, the total number of students = 12+8 = 20. Since 1/4 of the 8 juniors go on the trip, the number of juniors on the trip = (1/4)(8) = 2. Since 2/3 of the 12 seniors go on the trip, the number of seniors on the trip = (2/3)(12) = 8. Thus, the total number of students on the trip = 2+8 = 10. Resulting fraction: (total students on the trip)/(total number of students) = 10/20 = 1/2. The correct answer is B. _________________ 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 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip? (A) 4/9 (B) 1/2 (C) 2/3 (D) 1/3 (E) 5/6 The OA is B. I can understand this PS question. Can any expert explain it please? Thanks. Hi LUANDATO, Let's look at your question. If there are a total of 'x' seniors, then the juniors will be (2/3)x. Total students = seniors + juniors Total students = $$=x+\frac{2}{3}x=\frac{5}{3}x$$ The students going on the trip are: 1/4 of all juniors = $$\left(\frac{1}{4}\right)\left(\frac{2}{3}x\right)=\frac{1}{6}x$$ 2/3 of all seniors = $$\frac{2}{3}x$$ Total students going on the trip are: $$=\frac{1}{6}x +\frac{2}{3}x$$ $$=\left(\frac{1+4}{6\ }\right)x$$ $$=\left(\frac{5}{6\ }\right)x$$ Fraction of the students going on the trip = Students going on the trip / Total students $$=\frac{\frac{5}{6}x}{\frac{5}{3}x}$$ $$=\frac{5x\times3}{6\times5x}$$ $$=\frac{3}{6}$$ $$=\frac{1}{2}$$ We are asked to find the fraction of the students not going on the trip which can be calculated as: Fraction of the students not going on the trip = 1 - Fraction of the students going on the trip Fraction of the students not going on the trip = 1 - 1/2 = 1/2 Therefore, Option B is correct. Hope this helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 LUANDATO wrote: 1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip? (A) 4/9 (B) 1/2 (C) 2/3 (D) 1/3 (E) 5/6 We can let the total number of seniors = 36. Since there are 2/3 as many juniors, there are 24 juniors. Since 1/4 of the juniors are going on the trip, 1/4 x 24 = 6 juniors are going on the trip. Since 2/3 of the seniors are going on the trip, 2/3 x 36 = 24 seniors are going on the trip. Since there are a total of 36 + 24 = 60 students, and 60 - 6 - 24 = 30 are not going on the trip, we see that 1/2 of the students are not going on the trip. Answer: B _________________ 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. 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