BTGmoderatorDC wrote:On a wedding catering service, An experienced chef can prepare a service for a wedding in 8 hours while an novice chef would finish the preparations in 12 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Source: Economist GMAT
Excellent opportunity for UNITS CONTROL, one of the most powerful tools of our method!
\[\left. \begin{gathered}
{\text{N}}\,\,{\text{pros}}:\,\,\frac{{\,1 \cdot N\,\,{\text{services}}\,}}{{8\,\,{\text{hours}}}} = \frac{{\,\frac{N}{2}\,\,{\text{services}}\,}}{{4\,\,{\text{hours}}}}\,\,\,\,\,\, \hfill \\
{\text{N}}\,\,{\text{novs}}:\,\,\frac{{\,1 \cdot N\,\,{\text{services}}\,}}{{12\,\,{\text{hours}}}} = \frac{{\,\frac{N}{3}\,\,{\text{services}}\,}}{{4\,\,{\text{hours}}}} \hfill \\
\end{gathered} \right\}\,\,\,1\,\,{\text{service}}\,\,{\text{together}}\,\,{\text{in}}\,\,\,1{\text{h}}36\min \,\,\,\,;\,\,\,\,\,? = 2N\]
\[\left( {1 + \frac{{36}}{{60}}} \right)\,\,{\text{hours}}\,\,\,\left[ {\,\frac{{\,\left( {\frac{N}{2} + \frac{N}{3}} \right)\,\,{\text{services}}\,}}{{4\,\,{\text{hours}}}}\,} \right]\,\,\,\,\,\, = \,\,\,1\,\,\,{\text{service}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\frac{{96}}{{60 \cdot 4}}\,\,\left( {\frac{{N \cdot \boxed3}}{{2 \cdot \boxed3}} + \frac{{N \cdot \boxed2}}{{3 \cdot \boxed2}}} \right)\,\,\, = \,\,\,1\,\]
\[ \Rightarrow \,\,\,\,\,\,\frac{{24}}{{\,60\,}}\,\,\left( {\frac{{N \cdot \boxed3}}{{2 \cdot \boxed3}} + \frac{{N \cdot \boxed2}}{{3 \cdot \boxed2}}} \right)\,\,\, = \,\,\,1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\frac{{5N}}{6} = \frac{{60}}{{24}}\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,N = \frac{6}{5}\left( {\frac{{60}}{{24}}} \right) = 3\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,? = 2N = 6\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
