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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 ## At a certain school, the student to teacher ratio is 52 to 9 tagged by: Brent@GMATPrepNow ##### This topic has 2 expert replies and 1 member reply ### GMAT/MBA Expert ## At a certain school, the student to teacher ratio is 52 to 9 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 teachers D) 1418 students and 241 teachers E) 1728 students and 295 teachers Hint: One approach will allow you to solve the question in under 20 seconds. _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Brent@GMATPrepNow wrote: At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 teachers D) 1418 students and 241 teachers E) 1728 students and 295 teachers $$?\,\,\,:\,\,\,\left( {{\text{final}}\,\,S,{\text{final}}\,\,T} \right)\,\,\,\,\,\underline {{\text{possible}}}$$ $$\left\{ \matrix{ S\,\,:\,\,\,\,52k\,\,\,\,\, \to \,\,\,\,\,52k - 38 \hfill \cr T\,\,:\,\,\,\,9k\,\,\,\,\, \to \,\,\,\,\,9k - 11 \hfill \cr} \right.\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{final}}\,\,{\rm{sum}}\,\,{\rm{ = }}\,\,61k - 49\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {{\rm{final}}\,\,{\rm{sum}} + 49} \right)\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,61\,\,\,\,\left( * \right)$$ \eqalign{ & \left( A \right)\,\,532 + 88 + 49 = 669 = 610 + 59\,\,\,\, \Rightarrow \,\,\,\,{\rm{no}}! \cr & \left( B \right)\,\,794 + 162 + 49 = 1005 = 1220 - 15\,\,\,\, \Rightarrow \,\,\,\,{\rm{no}}! \cr & \left( C \right)\,\,1106 + 225 + 49 = 1380 = 1220 + 160\,\,\,\, \Rightarrow \,\,\,\,{\rm{no}}! \cr & \left( D \right)\,\,1418 + 241 + 49 = 1708 = 1220 + 488 = 1220 + 61 \cdot 8\,\,\,\, \Rightarrow \,\,\,\,{\rm{survivor}}! \cr & \left( E \right)\,\,1728 + 295 + 49 = 2072 = 2440 - 368 = 2440 - 366 - 2\,\,\,\, \Rightarrow \,\,\,\,{\rm{no}}! \cr} There is only one survivor, meaning the property (*) is good enough for our purposes! The correct answer is (D). 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 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Brent@GMATPrepNow wrote: At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 teachers D) 1418 students and 241 teachers E) 1728 students and 295 teachers Hint: One approach will allow you to solve the question in under 20 seconds. There's a nice integer properties rule that says: If j is a multiple of d, and k is NOT a multiple of d, then j-k (and j+k) is NOT a multiple of d For example, since 56 is a multiple of 7, and 11 is NOT a multiple of 7, then 56-11 is NOT a multiple of 7 At a certain school, the student to teacher ratio is 52 to 9. So, some possible scenarios are as follows: - there are 52 students and 9 teachers - there are 104 students and 18 teachers - there are 156 students and 27 teachers etc Notice that the number of students is always a multiple of 52. Since 52 is a multiple of 4, we can also see that the number of students is always a multiple of 4. Also notice that the number of teachers is always a multiple of 9. 38 students and 11 teachers leave Notice that 38 is NOT a multiple of 4 And 11 is NOT a multiple of 9 By the above property, the REMAINING number of students is NOT a multiple of 4 By the above property, the REMAINING number of teachers is NOT a multiple of 9 Which of the following COULD represent the number of students and teachers remaining at the school? Since the REMAINING number of students is NOT a multiple of 4, we can ELIMINATE answer choices A and E, since 532 and 1728 ARE multiples of 4 Since the REMAINING number of teachers is NOT a multiple of 9, we can ELIMINATE answer choices B and C, since 162 and 225 ARE multiples of 9 By the process of elimination, the correct answer is D 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! ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1097 messages Followed by: 2 members Student : Teacher => 52 : 9 Number of student = 52x (multiple of 4) Number of teacher = 9y (multiple of 9) 38 students and 11 teachers leave the school 38 is not a multiple of 4 11 is not a multiple of 9 Therefore, the remaining number of students are not a multiple of 4 Remaining number of teachers are not a multiple of 9 With this, option A and E will be eliminated because 532 and 1728 are multiples of 4 (number of students remaining) Option B and C will also be eliminated because 162 and 225 are multiples of 9 (number of teachers remaining) Therefore, correct answer = option D 1418 students = not a multiple of 4 241 students = not a multiple of 9 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for0

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