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If the line segment AB is one of the sides of a regular poly

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If the line segment AB is one of the sides of a regular poly

by fskilnik@GMATH » Wed Feb 27, 2019 5:44 pm

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GMATH practice exercise (Quant Class 15)

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Answer: [spoiler]____(A)__[/spoiler]
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Source: — Data Sufficiency |
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If the line segment AB is one of the sides of a regular poly

by fskilnik@GMATH » Thu Feb 28, 2019 6:12 am

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fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 15)

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$${\rm{regular}}\,\,N{\rm{ - polygon}}\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} } \right)$$
$$? = N$$

$$\left( 1 \right)\,\,\alpha = {30^ \circ }\,\,\,\, \Rightarrow \,\,\,\angle AOB = {60^ \circ }\,\,\,\left( {{\rm{central}}\,\,{\rm{angle}}} \right)\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,? = {{{{360}^ \circ }} \over {{{60}^ \circ }}} = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,2\pi r = 4\pi \,\,\, \Rightarrow \,\,\,r = 2\,\,\,:\,\,\left( {{\rm{images}}} \right)\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\alpha = {30^ \circ }\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,\,? = {{{{360}^ \circ }} \over {{{60}^ \circ }}} = 6\,\,\,\,\left( {{\rm{regular}}\,\,{\rm{hexagon}}} \right) \hfill \cr
\,{\rm{Take}}\,\,\alpha = {60^ \circ }\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,\,? = {{{{360}^ \circ }} \over {{{120}^ \circ }}} = 3\,\,\,\,\left( {{\rm{equilateral}}\,\,{\rm{triangle}}} \right) \hfill \cr} \right.$$


The correct answer is (A).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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