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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 ## For each positive integer n, the nth positive triangular num tagged by: fskilnik@GMATH ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## For each positive integer n, the nth positive triangular num ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 17) For each positive integer n, the nth positive triangular number is equal to the number of dots in the triangular arrangement with n dots on a side. The first positive triangular numbers are 1, 3, 6, 10, 15, and 21, as shown. Which of the following numbers is NOT a positive triangular number? (A) 105 (B) 210 (C) 300 (D) 311 (E) 378 Answer: ___(D)__ _________________ 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) For each positive integer n, the nth positive triangular number is equal to the number of dots in the triangular arrangement with n dots on a side. The first positive triangular numbers are 1, 3, 6, 10, 15, and 21, as shown. Which of the following numbers is NOT a positive triangular number? (A) 105 (B) 210 (C) 300 (D) 311 (E) 378 $${T_n} = 1 + 2 + \ldots + n\,\,\mathop = \limits^{\left( * \right)} \,\,{{n \cdot \left( {n + 1} \right)} \over 2}\,\,\,\,\,\,\,\left( {n \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\,\,\,\,\,\,\,\left[ {\left( * \right)\,\,{\rm{arithmetic}}\,\,{\rm{sequence}}} \right]$$ $$?\,\,\,:\,\,\,\underline {{\rm{not}}} \,\,\,{T_n}$$ $$\left( A \right)\,\,\left\{ \matrix{ \,n \cdot \left( {n + 1} \right) = 2 \cdot 105 = 210 \hfill \cr \,15 \cdot 15 = 225 \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{try}}!} \,\,\,\,{{14 \cdot 15} \over 2} = 7 \cdot 15 = 105\,\,\,{\rm{works}}!\,\,\,\,\, \Rightarrow \,\,\,\,\,105 = {T_{14}}$$ $$\left( B \right)\,\,\left\{ \matrix{ \,n \cdot \left( {n + 1} \right) = 2 \cdot 210 = 420 \hfill \cr \,20 \cdot 20 = 400 \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{try}}!} \,\,\,\,{{20 \cdot 21} \over 2} = 10 \cdot 21 = 210\,\,\,{\rm{works}}!\,\,\,\,\, \Rightarrow \,\,\,\,\,210 = {T_{20}}$$ $$\left( C \right)\,\,\left\{ \matrix{ n \cdot \left( {n + 1} \right) = 2 \cdot 300 = 600 \hfill \cr 25 \cdot 25 = 625 \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{try}}!} \,\,\,\,{{24 \cdot 25} \over 2} = 12 \cdot 25 = 300\,\,\,{\rm{works}}!\,\,\,\,\, \Rightarrow \,\,\,\,\,300 = {T_{24}}$$ $$\left( D \right)\,\,\,{T_{24}} < 311 < 300 + 25 = {T_{24}} + 25 = {T_{25}}$$ The correct answer is (D). 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 • FREE GMAT Exam Know how you'd score today for$0

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