Bunuel wrote:
What is the ratio of men to women enrolled in a certain class?
(1) The number of women enrolled in the class is 3 less than half the number of men enrolled.
(2) The number of women enrolled in the class is 2/5 of the number of men enrolled.
[Hi, Bunuel! Let me contribute to this simple but important problem.]
\(? = {m \over w}\,\,\,\,\,\,\,\left( {m,w\,\, \ge 1\,\,{\rm{ints}}} \right)\)
\(\left( 1 \right)\,\,w = {m \over 2} - 3\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {8,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{8}}\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {10,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{? }}\,{\rm{ = }}\,\,{\rm{5}}\,\, \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\)
\(\left( 2 \right)\,\,w = {2 \over 5}m\,\,\,\,\,\mathop \Rightarrow \limits^{w\,\, \ne \,\,0} \,\,\,\,\,{5 \over 2} = {m \over w} = ?\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}\)
The correct answer is therefore (B).
Regards,
Fabio.
P.S.:
Bunuel : please take out the typo (extra "2") in the statement (2).
Typo edited. Than you Fabio.