Bunuel wrote:
A conference room has two analog (12-hour format) clocks, one on the north wall and one on the south wall. The clock on the north wall loses 30 seconds per hour, and the clock on the south wall gains 15 seconds per hour. If the clocks begin displaying the same time, after how long will they next display the same time again?
A. 32 days
B. 36 days
C. 40 days
D. 44 days
E. 48 days
This is an excellent example of a problem in which "blending" two of our most powerful techniques solves the exercise immediately (in just one line)!
Techniques: Relative Velocity AND Units Control
\(\left\{ \begin{gathered}
{\text{North}}:\,\,\frac{{ - 30\,\,{\text{s}}}}{{1\,\,{\text{h}}}} \hfill \\
{\text{South}}:\,\,\frac{{ + 15\,\,{\text{s}}}}{{1\,\,{\text{h}}}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\, \sim \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( * \right)\,\,\,\left\{ \begin{gathered}
{\text{North}}:\,\,{\text{regular}}\,\,{\text{clock}} \hfill \\
{\text{South}}:\,\,\frac{{ + 45\,\,{\text{s}}}}{{1\,\,{\text{h}}}} \hfill \\
\end{gathered} \right.\)
\(?\,\,{\text{in}}\,\,\left( * \right)\,\,:\,\,\, + 12{\text{h}}\,\,\,\,{\text{in}}\,\,\,{\text{?}}\,\,{\text{h}}\)
Once DATA and FOCUS were structurally presented, let´s connect them! (This is our method´s "backbone".)
\(?\,\,\,\, = \,\,\,\, + {\text{12h}}\,\,\,\left( {\frac{{60 \cdot 60\,\,\,{\text{s}}}}{{1\,\,{\text{h}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\left( {\frac{{1\,\,{\text{h}}}}{{ + 45\,\,\,{\text{s}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\left( {\frac{{1\,\,{\text{day}}}}{{24\,\,{\text{h}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\, = \,\,\,\,\,\frac{{12 \cdot 60 \cdot 60}}{{45 \cdot 24}} = 40\,\,{\text{days}}\)
Obs.: arrows indicate licit converters.
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
P.S.: many solutions presented before had exactly the same rationale, by the way.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here:
https://gmath.net