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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 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: 1449 messages Followed by: 32 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 :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2424 messages Followed by: 18 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 scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 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 • FREE GMAT Exam Know how you'd score today for$0

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