GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 23:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If the line segment AB is one of the sides of a regular polygon inscri

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
If the line segment AB is one of the sides of a regular polygon inscri  [#permalink]

### Show Tags

27 Feb 2019, 18:48
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:47) correct 45% (01:40) wrong based on 22 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 15)

If the line segment AB is one of the sides of a regular polygon inscribed in the given circle with center O, how many sides does this polygon have?

(1) $$\,\alpha = {30^ \circ }$$.
(2) The circumference of the circle is equal to$$\,4\pi \,$$.

Attachment:

27-Feb19-8r.gif [ 8.99 KiB | Viewed 333 times ]

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If the line segment AB is one of the sides of a regular polygon inscri  [#permalink]

### Show Tags

28 Feb 2019, 07:22
fskilnik wrote:
GMATH practice exercise (Quant Class 15)

If the line segment AB is one of the sides of a regular polygon inscribed in the given circle with center O, how many sides does this polygon have?

(1) $$\,\alpha = {30^ \circ }$$.
(2) The circumference of the circle is equal to$$\,4\pi \,$$.

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

$$? = N$$

$$\left( 1 \right)\,\,\alpha = {30^ \circ }\,\,\,\, \Rightarrow \,\,\,\angle AOB = {60^ \circ }\,\,\,\left( {{\rm{central}}\,\,{\rm{angle}}} \right)\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{regularity}}} \,\,\,\,\,? = {{{{360}^ \circ }} \over {{{60}^ \circ }}} = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

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

We follow 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
Re: If the line segment AB is one of the sides of a regular polygon inscri   [#permalink] 28 Feb 2019, 07:22
Display posts from previous: Sort by