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Which of the following is closest to the distance traveled by the tip

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Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 05 Sep 2018, 00:21
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  35% (medium)

Question Stats:

69% (01:11) correct 31% (01:31) wrong based on 13 sessions

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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

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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 05 Sep 2018, 01:57
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Bunuel wrote:
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



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
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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 05 Sep 2018, 10:10
Bunuel wrote:
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


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.

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fskilnik.
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Re: Which of the following is closest to the distance traveled by the tip  [#permalink]

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New post 05 Sep 2018, 11:20
Before you do the math here, estimate. The answer choices are pretty spread out, so why waste time being accurate?

Restate the question as "What is 1/3 of the circumference of a circle with a radius of 3?"

Circumference = 2 pi r
So a third would be (2 pi 3 )/3
You are estimating, so cancel out the 3 and the 3.
2 pi = 6 ish.

The right answer is around 6. Go with D.

Jayson Beatty
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Re: Which of the following is closest to the distance traveled by the tip &nbs [#permalink] 05 Sep 2018, 11:20
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