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05 Sep 2018, 00:21
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
79% (01:38) correct
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Which of the following is closest to the distance traveled by the tip of a 3-inch minute hand of a clock in 17 minutes?
A. 17 inches
B. 10 inches
C. 8 inches
D. 5 inches
E. 1 inches
A. 17 inches
B. 10 inches
C. 8 inches
D. 5 inches
E. 1 inches
05 Sep 2018, 01:57
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Bunuel
there are a total of 60 minutes in 360 degrees of the clock
so each minute = 6 degrees
therefore, in 17 minutes we have 6*17=102 degrees
distance = length of arc formed by the minute hand with radius 3
= 2\(\pi\)*3 *\(\frac{102}{360}\)= \(\pi\)*\(\frac{102}{60}\)= 5.338
05 Sep 2018, 10:10
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Bunuel
Excellent problem to practice:
(1) UNITS CONTROL (one of our most powerful tools)!
(2) Arithmetic skills, in particular a famous (and very useful in the GMAT) Pi approximation (22/7)
\(?\,\,\,:\,\,\,\# \,\,{\text{in}}\,\,\left( {{\text{approx}}{\text{.}}} \right)\,\,\,{\text{for}}\,\,17\min\)
\(?\,\,\, = \,\,\,17\min \,\,\left( {\frac{{1\,\,{\text{round}}}}{{60\,\min }}\,\,\begin{array}{*{20}{c}}\\
\nearrow \\ \\
\nearrow \\
\end{array}} \right)\,\,\left( {\frac{{2\pi \cdot 3\,\,{\text{in}}}}{{1\,\,{\text{round}}}}\,\,\begin{array}{*{20}{c}}\\
\nearrow \\ \\
\nearrow \\
\end{array}} \right)\,\,\, = \,\,\,\frac{{17 \cdot 2\pi \cdot 3}}{{60}}\,\,\,{\text{in}}\)
\(? = \frac{{17 \cdot 2\pi \cdot 3}}{{60}}\,\, \cong \,\,\,\frac{1}{{10}}\left( {\frac{{17 \cdot 22}}{7}} \right)\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\frac{1}{{10}}\left( {53\frac{3}{7}} \right)\,\,\, \cong \,\,\,\boxed{5.3}\)
\(\left( * \right)\,\,\,\frac{{17 \cdot 22}}{7} = \frac{{340 + 34}}{7}\,\,\, = \,\,\,\frac{{350 + 21 + 3}}{7} = 53\frac{3}{7}\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
