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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 ## When m is divided by 7, the remainder is 5. When m is tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## When m is divided by 7, the remainder is 5. When m is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Economist GMAT When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m? A. 5 B. 19 C. 61 D. 74 E. 110 The OA is E. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that when M is divided by 7, the remainder is 5, when M is divided by 13, the remainder is 6 and 1 < m < 200. We're asked for the GREATEST possible value of M. This question can be solved rather easily by TESTing THE ANSWERS. Let's TEST Answer E first (if it fits what we're told, then we're done; if it does not fit, then we'll Test Answer D and so on). Answer E: 110 110/7 = 15r5 --> this fits what we're told 110/13 = 8r6 --> this also fits what we're told Thus, this must be the answer. Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: Economist GMAT When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m? A. 5 B. 19 C. 61 D. 74 E. 110 $? = {m_{\,\max }}\,\,\,\left( {1 < m < 200} \right)\,\,{\text{such}}\,\,{\text{that}}\,\,\,\,\left\{ \begin{gathered} m = 7Q + 5\,\,\,\left( 1 \right)\,\, \hfill \\ m = 13K + 6\,\,\,\left( 2 \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\left( {Q,K\,\,\,{\text{ints}}} \right)$ $\left\{ \begin{gathered} \left( 1 \right) \cdot 13\,\,\,\, \Rightarrow \,\,\,\,13m = 7 \cdot 13Q + 65 \hfill \\ \left( 2 \right) \cdot 7\,\,\,\,\,\, \Rightarrow \,\,\,\,7m = 7 \cdot 13K + 42 \hfill \\ \end{gathered} \right.\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,6m = 7 \cdot 13\left( {Q - K} \right) + 23$ $\left\{ \begin{gathered} \,7m = 7 \cdot 13K + 42 \hfill \\ \,6m = 7 \cdot 13\left( {Q - K} \right) + 23 \hfill \\ \end{gathered} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,m = 7 \cdot 13\left( {2K - Q} \right) + 19$ $\left\{ \begin{gathered} \,m = 91J + 19 \hfill \\ \,1 < m < 200 \hfill \\ \end{gathered} \right.\,\,\,\,\left( {J\,\,\operatorname{int} } \right)\,\,\,\, \Rightarrow \,\,\,\,\,{J_{\max }} = 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {m_{\,\max }} = 91 + 19 = 110$ 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: 2791 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Economist GMAT When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m? A. 5 B. 19 C. 61 D. 74 E. 110 The OA is E. We are given two properties about m: when m is divided by 7, the remainder is 5; further, when m is divided by 13, the remainder is 6. We can create the following two equations: m = 7q+ 5 for some nonnegative integer q According to the above expression, m can be: 5, 12, 19, ... m = 13z + 6 for some nonnegative integer z According to the above expression, m can be: 6, 19, 32, â€¦ We can see that 19 is the smallest positive integer value of m that satisfies the properties. However, we are asked to find the largest integer less than 200 that satisfies the properties. In that case, we can add 19 to any number that is both divisible by 13 and 7, in other words, a number that is a multiple of both 13 and 7. Since the LCM of 13 and 7 is 13 x 7 = 91, the next value of m is 19 + 91 = 110, which happens to be the largest possible value of m that is still less than 200. (Note: the next value of m is 110 + 91 = 201, which is greater than 200.) Alternate solution: The problem is asking for the largest possible value less than 200 that satisfies the following properties: when m is divided by 7, the remainder is 5, and when m is divided by 13, the remainder is 6. We can check the largest number in the given answer choices first and work backward until we find the answer. So letâ€™s check 110 first: 110/7 = 15 R 5 and 110/13 = 8 R 6 We see that 110 satisfies both properties, so 110 is the answer. . Answer: E _________________ 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 • Award-winning private GMAT tutoring Register now and save up to$200

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