GinGMAT wrote:
The average (arithmetic mean) cost of three computer models is $900. If no two computers cost the same amount, does the most expensive model cost more than $1,000?
(1) The most expensive model costs 25% more than the model with the median cost.
(2) The most expensive model costs $210 more than the model with the median cost.
\({\rm{costs}}\,\,:\,\,a < b < c\,\,\,\,\,\,\left[ \$ \right]\)
\(a + b + c = 3 \cdot 900 = 2700\,\,\,\left( * \right)\)
\(c\,\,\mathop > \limits^? \,\,1000\)
\(\left( 1 \right)\,\,c = {5 \over 4}b\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,a + {9 \over 5}c = 2700\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\)
\(\left( {**} \right)\,\,\,\,c \le 1000\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,{9 \over 5}c\,\, \le \,\,1800\,\,\,\,\, \Rightarrow \,\,\,\,\,a = 2700 - {9 \over 5}c\,\, \ge \,\,2700 - 1800 = 900 \hfill \cr
\,b = {4 \over 5}c\,\, \le \,\,800 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,b \le 800 < 900 \le a\,\,\,{\rm{impossible}}\)
\(\left( 2 \right)\,\,c - b = 210\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,a + \left( {c - 210} \right) + c = 2700\,\,\,\,\, \Rightarrow \,\,\,\,\,a + 2c = 2910\,\,\,\,\mathop \Rightarrow \limits^{\left( {***} \right)} \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.\)
\(\left( {***} \right)\,\,\,\,c \le 1000\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,a = 2910 - 2c\,\, \ge \,\,2910 - 2000 = 910 \hfill \cr
\,b = c - 210\,\, \le \,\,790 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,b \le 790 < 910 \le a\,\,\,{\rm{impossible}}\)
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Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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58% (02:45) correct 
