Claudio wants to be well prepared for a long marathon that w

Question

GMATH practice exercise (Quant Class 17) Claudio wants to be well prepared for a long marathon that will occur in the near future. His running coach has decided that the training sessions must be done once every two days, starting with a 15-kilometer distance route, and adding exactly 500 meters (=half a kilometer) to the route at every new training session. Claudio´s coach believes at least 1800 kilometers must be run, during the whole training period, before someone is considered ready for this challenge. According to these assumptions, what is the minimum number of training sessions that Claudio needs for this long marathon preparation? (A) 59 (B) 60 (C) 61 (D) 62 (E) 63 Answer: [spoiler]_____(C)__[/spoiler]

fskilnik@GMATH · Answer

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 17) Claudio wants to be well prepared for a long marathon that will occur in the near future. His running coach has decided that the training sessions must be done once every two days, starting with a 15-kilometer distance route, and adding exactly 500 meters (=half a kilometer) to the route at every new training session. Claudio´s coach believes at least 1800 kilometers must be run, during the whole training period, before someone is considered ready for this challenge. According to these assumptions, what is the minimum number of training sessions that Claudio needs for this long marathon preparation? (A) 59 (B) 60 (C) 61 (D) 62 (E) 63 $$?\,\,\,:\,\,\,\min \,N\,\,{\rm{for}}\,\,{\rm{sum}}\,\,\, \ge \,\,\,1800\,$$ $$\left. \matrix{ {a_1} = 15 \hfill \cr {a_2} = 15 + 1 \cdot {1 \over 2} \hfill \cr {a_3} = 15 + 2 \cdot {1 \over 2} \hfill \cr \vdots \hfill \cr {a_N} = 15 + \left( {N - 1} \right) \cdot {1 \over 2}\,\,\, \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{Arith}}{\rm{. Seq}}{\rm{.}}} \,\,\,\,\,1800\,\, \le \,\,\,\,N \cdot {1 \over 2}\left[ {15 + 15 + {{\left( {N - 1} \right)} \over 2}} \right] = {{N\left( {N + 59} \right)} \over 4}$$ $${\rm{Trying}}\,\,\left( B \right)\,\,N = 60\,\,\,\,\, \Rightarrow \,\,\,\,\,{{N\left( {N + 59} \right)} \over 4} = {{{{60}^2} + 60\left( {60 - 1} \right)} \over 4} = {{2 \cdot 3600 - 60} \over 4} = 1800 - 15\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\left( C \right)$$ $$\left( * \right)\,\,N = 61\,\,\,\,\, \Rightarrow \,\,\,\,{{N\left( {N + 59} \right)} \over 4}\,\, = \,\,\,\underbrace {1800 - 15}_{{\rm{sum}}\,\,{\rm{for}}\,\,N\,\, = \,\,60}\,\,\, + \,\,\underbrace {15 + 60 \cdot {1 \over 2}}_{{a_{61}}}\,\,\, = 1830\,\, > \,\,1800$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Claudio wants to be well prepared for a long marathon that w

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER