If Jim drives k miles in 50 minutes, how many minutes will

[BTGmoderatorLU]

Source: Princeton Review

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

The OA is A.

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Hi All,

We're told that Jim drives K miles in 50 MINUTES. We're asked how many MINUTES it will take him to drive 10 miles at the same rate. This question can be solved rather easily by TESTing VALUES.

Since K can be any positive value, we can set K = 10. Thus, we know that Jim drives 10 miles in 50 minutes. The question asks how minutes Jim drives 10 miles.... so the answer is 50. Thus, we're looking for an answer that equals 50 when K=10. Only one answer matches...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

[fskilnik@GMATH]

Source: Princeton Review

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

\[k\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{50}}\,\,{\text{minutes}}\,\,\,\,\,\,\,{\text{;}}\,\,\,\,\,\,\,\,{\text{10}}\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{?}}\,\,{\text{minutes}}\]
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.

[Scott@TargetTestPrep]

Source: Princeton Review

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

Since rate = distance/time, Jim's rate is k/50. We need to determine how many minutes it will take Jim to drive 10 miles.

time = distance/rate

time = 10/(k/50) = 10 x (50/k) = 500/k

Alternate Solution:

Letting x = the number of minutes it takes Jim to drive 10 miles, we can create the proportion:

k/50 = 10/x

kx = 500

x = 500/k

Answer: A