BTGmoderatorLU wrote:Source: Manhattan Prep

If Nicole worked 20% more this week than she worked last week, how many hours did she work last week?

1) Nicole worked 36 hours this week.
2) Nicole worked 6 more hours this week than she worked last week.

$${\rm{this}}\,\, = \,\,{\rm{\# }}\,\,{\rm{h}}\,\,{\rm{Nicole}}\,\,{\rm{worked}}\,\,{\rm{this}}\,\,{\rm{week}}$$
$${\rm{last}}\,\, = \,\,{\rm{\# }}\,\,{\rm{h}}\,\,{\rm{Nicole}}\,\,{\rm{worked}}\,\,{\rm{last}}\,\,{\rm{week}}$$
$${\rm{this}}\,\,{\rm{ = }}\,\,{6 \over 5}\left( {{\rm{last}}} \right)\,\,\,\,\,\left( * \right)\,$$
$$? = {\rm{last}}$$
$$\left( 1 \right)\,\,{\rm{this}} = 36\,\,\mathop = \limits^{\left( * \right)} \,\,{6 \over 5}\left( {{\rm{last}}} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = {5 \over 6}\left( {36} \right)\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( 2 \right)\,\,{\rm{this}} - {\rm{last}} = 6\,\,\,\left[ {\rm{h}} \right]\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{6 \over 5}\left( {{\rm{last}}} \right) - {\rm{last}} = {1 \over 5}\left( {{\rm{last}}} \right) = {\rm{6}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 5 \cdot 6\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$

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

Regards,
Fabio.