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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 ## A law school admissions office sent letters to each of its tagged by: AAPL ##### This topic has 2 expert replies and 1 member reply ### Top Member ## A law school admissions office sent letters to each of its ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Veritas Prep A law school admissions office sent letters to each of its 200 applicants, but because of an error in the mail room the acceptance and denial letters did not all go to the proper recipients. 40% of those who should have received denial letters received acceptance letters instead, and 10% of those who were supposed to receive acceptances received denial letters. If 160 applicants received acceptance letters, how many applicants who should have received acceptance letters instead received denial letters? A. 16 B. 20 C. 24 D. 28 E. 32 OA A ### Top Member Junior | Next Rank: 30 Posts Joined 03 Oct 2018 Posted: 10 messages Let x be the number of applicants who should have received acceptance letters. Let y be the number of applicants who should have received denial letters. Therefore we know that x+y=200 Now, 10% of those who were supposed to receive acceptances received denial letters. This means that 90% of the accepted candidates got their correct letters, which is 0.9x. 40% of those who should have received denial letter got acceptance letters instead, which is 0.4y Since 160 applicants received acceptance letters 0.9x+0.4y=160. Now we can solve the 2 equations Solve this we have x=160 and y=40. Thus 0.1x = 16 ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 707 messages Followed by: 26 members Upvotes: 59 AAPL wrote: Veritas Prep A law school admissions office sent letters to each of its 200 applicants, but because of an error in the mail room the acceptance and denial letters did not all go to the proper recipients. 40% of those who should have received denial letters received acceptance letters instead, and 10% of those who were supposed to receive acceptances received denial letters. If 160 applicants received acceptance letters, how many applicants who should have received acceptance letters instead received denial letters? A. 16 B. 20 C. 24 D. 28 E. 32 Another very nice problem in which "blending" the k technique and the grid (double-matrix) "shields" the problem fast and clear! (At least to my students) Study this problem asking yourself why start putting in the grid the 10k "value" was a smart move. $$? = {1 \over {10}}\left( {200 - 10k} \right) = 20 - k$$ $$160 - {2 \over 5}\left( {10k} \right) = {9 \over {10}}\left( {200 - 10k} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,160 - 4k = 180 - 9k\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,5k = 20$$ $$? = 16$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: www.GMATH.net (Math for the GMAT) Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1649 messages Followed by: 14 members Upvotes: 43 AAPL wrote: Veritas Prep A law school admissions office sent letters to each of its 200 applicants, but because of an error in the mail room the acceptance and denial letters did not all go to the proper recipients. 40% of those who should have received denial letters received acceptance letters instead, and 10% of those who were supposed to receive acceptances received denial letters. If 160 applicants received acceptance letters, how many applicants who should have received acceptance letters instead received denial letters? A. 16 B. 20 C. 24 D. 28 E. 32 We can let r = the number of applicants who should have received acceptance letters; thus, (200 - r) = the number of applicants who should have received denial letters. Thus, 0.9r = the number of applicants who should have received acceptance letters and received acceptance letters, and 0.1r = the number of applicants who should have received acceptance letters but received denial letters instead. Similarly, 0.6(200 - r) = the number of applicants who should have received denial letters and received denial letters, and 0.4(200 - r) = the number of applicants who should have received denial letters but received acceptance letters instead. Therefore, we can create the following equation for the total number of applicants who received acceptance letters: 0.9r + 0.4(200 - r) = 160 9r + 4(200 - r) = 1600 9r + 800 - 4r = 1600 5r = 800 r = 160 Since 10% of the 160 applicants who should have received acceptance letters received denial letters, 16 of them received denial letters. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO • 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 • 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 • Magoosh Study with Magoosh GMAT prep 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

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