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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 ## There are many boxes in a certain room, and each box has a l tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## There are many boxes in a certain room, and each box has a l ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 17) There are many boxes in a certain room, and each box has a label attached to it in which the number of balls contained in that box is written. If there are exactly 612 balls in all boxes combined, and it is known that the numbers presented at the labels form a sequence of the first N consecutive positive multiples of 4, the value of N is: (A) divisible by 3 (B) divisible by 7 (C) divisible by 11 (D) divisible by 13 (E) prime Answer: _____(E)__ _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 17) There are many boxes in a certain room, and each box has a label attached to it in which the number of balls contained in that box is written. If there are exactly 612 balls in all boxes combined, and it is known that the numbers presented at the labels form a sequence of the first N consecutive positive multiples of 4, the value of N is: (A) divisible by 3 (B) divisible by 7 (C) divisible by 11 (D) divisible by 13 (E) prime $$4 \cdot 1 + 4 \cdot 2 + \ldots + 4 \cdot N = 612$$ $$? = N\,\,\,\,\left( {N \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\left( * \right)$$ $$612 = 4(1 + 2 + \ldots + N)\,\,\,\mathop = \limits^{{\rm{Arith}}{\rm{.Seq}}} \,\,\,4\left[ {{{N\left( {N + 1} \right)} \over 2}} \right]\,\, = \,\,2N\left( {N + 1} \right)$$ $$N\left( {N + 1} \right) = 306 = 2 \cdot {3^2} \cdot 17\,\,\left[ { = 17 \cdot 18} \right]\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,N = 17$$ The correct answer is (E). We follow 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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