SajjadAhmad wrote:

If Jim drives k miles in 50 minutes, how many minutes will it take him to drive 10 miles, at the same rate?

A. 500/k

B. k/500

C. 60k

D. 10k

E. 50/k

\(k\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{50}}\,\,{\text{minutes}}\,\,\,\,\,\,\,\)

\({\text{10}}\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{?}}\,\,{\text{minutes}}\)

This is a (direct) proportional problem, therefore a 10-year-child would probably do it (correctly) like that:

\(\frac{?}{{50}} = \frac{{10}}{k}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{500}}{k}\)

On the other hand, this is a trivial scenario for UNITS CONTROL, one of the most powerful tools of our method:

\(?\,\,\, = \,\,\,10\,\,{\text{miles}}\,\,\,\left( {\frac{{50\,\,{\text{minutes}}}}{{k\,\,{\text{miles}}}}\begin{array}{*{20}{c}}

\nearrow \\

\nearrow

\end{array}} \right)\,\,\,\, = \,\,\,\,\frac{{500}}{k}\,\,\,\,\left[ {{\text{minutes}}} \right]\)

Obs.: arrows indicate licit converter.

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

Regards,

Fabio.

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)

Our high-level "quant" preparation starts here: https://gmath.net