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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 ## Numbers Question tagged by: Brent@GMATPrepNow ##### This topic has 4 expert replies and 0 member replies ## Numbers Question ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A school administrator will assign each student in a group on n students to one of m classes.If 3 1) It is possible to assign each of the 3n students to one of m classes so that each classroom has the same number of students assigned to it. 2)It is possible to assign each of the 13n students to one of m classes so that each classroom has the same number of students assigned to it. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15342 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Quote: A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it? (1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it. (2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it. To assign the same number of students to each classroom, the number of students (n) must be divisible by the number of classrooms (m). Question rephrased: Is n/m an integer? Statement 1: It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it. In other words, the number of students (3n) is divisible by the number of classrooms (m). Implication: (3n)/m = 3(n/m) = integer. Case 1: n/m = integer It's possible that n=16 and m=4, with the result that n/m = 16/4 = 4. Here, 3(n/m) = 3(16/4) = 12. Case 2: n/m = k/3, where k is not a multiple of 3 In this case, since n/m = k/3, m must be a multiple of 3. It's possible that n=14 and m=6, with the result that n/m = 14/6 = 7/3. Here, 3(n/m) = 3(7/3) = 7. Since n/m is an integer in Case 1 but not in Case 2, INSUFFICIENT. Statement 2: It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it. In other words, the number of students (13n) is divisible by the number of classrooms (m). Implication: (13n)/m = 13(n/m) = integer. Case 3: n/m = integer It's possible that n=16 and m=4, since 16/4 = 4. Here, 13(n/m) = 13(16/4) = 52. Case 4: n/m = k/13, where k is not a multiple of 13 In this case, since n/m = k/13, m must be a multiple of 13. Not possible, since 3 < m < 13. Since only Case 3 is possible, n/m = integer. SUFFICIENT. 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 08 Dec 2008 Posted: 12975 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Quote: A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it? (1) It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it. (2) It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it. Target question: Is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it This is a great candidate for rephrasing the target question (more info about rephrasing the target question can be found in this free video: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100) In order to be able to assign the same number of students to each classroom, the number of students (n) must be divisible by the number of classrooms (m). In other words, n/m must be an integer. REPHRASED target question: Is n/m an integer? Statement 1: It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students to it. This statement is telling us that the number of students (3n) is divisible by the number of classrooms (m). In other words, 3n/m is an integer. Does this mean mean that m/n is an integer? No. Consider these contradictory cases. case a: m = 4 and n = 20, in which case n/m is an integer. case b: m = 6 and n = 20, in which case n/m is not an integer. Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students to it This statement tells us that the number of students (13n) is divisible by the number of classrooms (m). In other words, 13n/m is an integer. The given information tells us that 3 < m < 13 < n. Since m is between 3 and 13, there's no way that 13/m can be an integer. In fact, we can't even reduce the 13/m to simpler terms. From this, we can conclude that n/m must be an integer. Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT Answer = B For even more information on rephrasing the target question, you can read this article I wrote for BTG: http://www.beatthegmat.com/mba/2014/06/30/rephrasing-the-target-question 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! ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1465 messages Followed by: 18 members Upvotes: 39 aditiniyer wrote: A school administrator will assign each student in a group on n students to one of m classes.If 3 1) It is possible to assign each of the 3n students to one of m classes so that each classroom has the same number of students assigned to it. 2)It is possible to assign each of the 13n students to one of m classes so that each classroom has the same number of students assigned to it. We are given that each student in a group of n students is going to be assigned to one of m classrooms. We are being asked whether it is possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students. Thus, we need to determine whether n/m = integer. Statement One Alone: It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it. Statement one is telling us that 3n is evenly divisible by m. Thus, 3n/m = integer. However, we still do not have enough information to answer the question. When n = 16 and m = 4, n/m DOES equal an integer; however, when n = 20 and m = 6, n/m DOES NOT equal an integer. Statement Two Alone: It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it. This statement is telling us that 13n is divisible by m. Thus, 13n/m = integer. What is interesting about this statement is that we know that n is greater than 13 and that m is less than 13 and greater than 3. Thus, we know that m could equal any of the following: 4, 5, 6, 7, 8, 9, 10, 11, or 12. We see that none of those values (4 through 12) will divide evenly into 13. Knowing this, we can say conclusively that m will never divide evenly into 13. Thus, in order for m to divide into 13n, m must divide evenly into n. Answer: B _________________ Jeffrey Miller Head of GMAT Instruction jeff@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 aditiniyer wrote: A school administrator will assign each student in a group on n students to one of m classes.If 3 1) It is possible to assign each of the 3n students to one of m classes so that each classroom has the same number of students assigned to it. 2)It is possible to assign each of the 13n students to one of m classes so that each classroom has the same number of students assigned to it. Hi aditiniyer, We already have great solutions to the question. Here's my take on this question... We have to see if n/m is an integer. Let's take each statement one by one. S1: It is possible to assign each of the 3n students to one of m classes so that each classroom has the same number of students assigned to it. => (3n)/m = 3*(n/m) is integer. Say 3*(n/m) = k; where k in a positive integer => n/m = k/3 If k = 4, n/m is not an integer. The answer is NO. If k = a multiple of 3, n/m is an integer. The answer is YES. No unique answer. S2: It is possible to assign each of the 13n students to one of m classes so that each classroom has the same number of students assigned to it. => (13n)/m = 13*(n/m) is integer. 13*(n/m) = k; where k in a positive integer In order to get k, a positive integer, either m is a multiple of 13 or k is a multiple of 13. But we are given that m < 13, so it's not possible. Thus, k must be a multiple of 13, making n/m an integer. Sufficient. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Hyderabad | Mexico City | Toronto | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. If k = a multiple of 3, n/m is an integer. The answer is YES. 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