Data Sufficiency

A restaurant serves only tacos and enchiladas. If 60% of all who ate at the restaurant on a certain day ordered tacos, what percentage of those who ate at the restaurant ordered enchiladas that day?

(1) Half of those who ordered tacos also ordered enchiladas.
(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.

Anaira Mitch wrote:A restaurant serves only tacos and enchiladas. If 60% of all who ate at the restaurant on a certain day ordered tacos, what percentage of those who ate at the restaurant ordered enchiladas that day?

(1) Half of those who ordered tacos also ordered enchiladas.
(2) 3/4 as many people ordered both enchiladas and tacos as ordered only enchiladas.

$$? = x\,\,\,\,\left( {{\rm{see}}\,\,{\rm{figure}}} \right)$$



$$\left( 1 \right)\,\,\,\left[ {{\rm{Blue}}} \right]\,\,\,100 = 60 + x - 30\,\,\,\left( {{\rm{simplifier}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

$$\left( 2 \right)\,\,\,\left[ {{\rm{Red}}} \right]\,\,\,\,\left\{ \matrix{
{3 \over 4}\left( {x - {\rm{both}}} \right) = {\rm{both}}\,\,\,\,\,\left( {\rm{I}} \right) \hfill \cr
100 = 60 + \left( {x - {\rm{both}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,40 = x - {\rm{both}}\,\,\,\,\,\left( {{\rm{II}}} \right)\,\,\, \hfill \cr} \right.$$
$$\left( {\rm{I}} \right)\,\,{\rm{in}}\,\,\left( {{\rm{II}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,40 = {4 \over 3}\left( {{\rm{both}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{both}} = 30\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {{\rm{II}}} \right)} \,\,\,\,\,\,x\,\,{\rm{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.