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

It is currently 24 Sep 2018, 16:26

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A polygon is regular if all the sides are equal and all the interior a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 21 Feb 2018
Posts: 23
A polygon is regular if all the sides are equal and all the interior a  [#permalink]

Show Tags

New post Updated on: 12 Jul 2018, 21:02
3
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

13% (01:06) correct 87% (01:48) wrong based on 15 sessions

HideShow timer Statistics

A polygon is regular if all the sides are equal and all the interior angles are equal. Two sides of regular octagon O lie on lines l and m, respectively. If l and m intersect, what is the angle of intersection as measured facing in toward the octagon?

(1) Lines l and m do not intersect at a vertex of O
(2) A line bisecting the angle of intersection of l and m also bisects an interior angle of O.


Answer is C, but I cant visually picture the explanation of why 1 and two are insufficient in my head.. please help! Thanks.

Answer:
This is a Value Data Sufficiency question, so use the Pieces of the Puzzle approach to assess the question. Determine “What is known” from the question stem and “What is needed” from the statements to answer the question. Begin by determining “What is known.” The question states that O is a regular octagon and lines l and m on the octagon intersect. Since this is a geometry question, draw a figure to see how lines l and m could intersect. There are three distinct angles at which the line could intersect. If the sides of the octagon were numbered 1–8 clockwise starting from the top, (1) Lines l and m could lie on sides 1 and 2 and intersect at the adjoining vertex, forming the obtuse interior angle of the octagon. (2) Lines l and m could lie on sides 1 and 3, and they would intersect at a right angle outside of the octagon. (3) Lines l and m could lie on sides 1 and 4, and they would intersect at an acute angle outside the octagon. All of the other side combinations simply repeat these three angles. Now, determine “What is needed.” To answer the question, the statements must provide sufficient information to determine which of the three general combinations of sides of the octagon lines l and m represent. Evaluate the statements one at a time.

Evaluate Statement (1). Statement (1) provides lines l and m do not intersect at a vertex. This removes one of the three possible angle combinations, but there is no way to determine in which of the other two combinations lines l and m intersect. Therefore, Statement (1) is insufficient. Write down BCE.

Now, evaluate Statement (2). Statement (2) provides that a line bisecting the angle of intersection of l and m also bisects an interior angle of O. Draw the bisecting line for each of the intersection combinations to see which ones satisfy the statement. When lines l and m intersect at a vertex, the bisecting line also bisects the opposite vertex of O. When lines l and m intersect at a right angle, the line bisecting the angle bisects two sides of the octagon, not an interior angle. And when lines l and m intersect at an acute angle, the bisecting line bisects two interior angles of O. Therefore, there are two different angle combinations that satisfy the statement, lines l and m intersecting at a vertex or intersecting at an acute angle outside the octagon. Thus, Statement (2) is insufficient. Eliminate choice B.

Now, evaluate both statements together. Based on the information in Statement (2), lines l and m must intersect at a vertex or at an acute angle outside the octagon, but Statement (1) states that they do not intersect at a vertex. Therefore, the only angle combination that satisfies both statements is lines l and m intersecting at an acute angle outside the octagon. Do not solve for the value of the angle. Since only one angle satisfies both of the statements, the two statements together produce a consistent answer to the question.

The correct answer is choice C.

Originally posted by franteraoka on 12 Jul 2018, 15:02.
Last edited by Bunuel on 12 Jul 2018, 21:02, edited 1 time in total.
Edited the question and added the OA.
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 860
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
Re: A polygon is regular if all the sides are equal and all the interior a  [#permalink]

Show Tags

New post 13 Jul 2018, 08:27
1
1
[quote="franteraoka"]A polygon is regular if all the sides are equal and all the interior angles are equal. Two sides of regular octagon O lie on lines l and m, respectively. If l and m intersect, what is the angle of intersection as measured facing in toward the octagon?

(1) Lines l and m do not intersect at a vertex of O
(2) A line bisecting the angle of intersection of l and m also bisects an interior angle of O.

Please refer the affixed diagram.
There are 3 cases when two sides of the regular octagon lies on the line l and m and they intersect each other.

Case-1
1 and 2 intersect, they make a right angle out side the octagon.
Case-2
4 and 5 intersect, they make an obtuse angle at the interior of the octagon.
Case-3
6 and 1 intersect, they make an acute angle at the out side the octagon.
N.B:- All intersecting angles are considered facing towards the octagon as per given condition.

Question stem:- Measure of angle of intersection=?

Statement-1:- Lines l and m do not intersect at a vertex of O
Case-2 is eliminated since the lines meet at vertex "E".
Case-1 & 3 are valid. So, we have more than one measure of required angle.
Hence, insufficient.

Statement-2:- A line bisecting the angle of intersection of l and m also bisects an interior angle of O.
Case-1 is eliminated since the line bisecting the angle of intersection of 'l' and 'm' doesn't bisect the interior angle of octagon rather bisects the pair of opposite sides.
Case-2 & 3 are valid. So, we have more than one measure of required angle.
Hence, insufficient.

Combining st1 & st2, we have , only case-3 ,which is valid in both the circumstances.
Hence, we have one measure of angle of intersection.

Therefore sufficient.

Ans. (C)
Attachments

Octagon.JPG
Octagon.JPG [ 38.43 KiB | Viewed 240 times ]


_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Intern
Intern
avatar
B
Joined: 21 Feb 2018
Posts: 23
Re: A polygon is regular if all the sides are equal and all the interior a  [#permalink]

Show Tags

New post 13 Jul 2018, 09:06
Thank you so much!PKN
Director
Director
User avatar
P
Status: Learning stage
Joined: 01 Oct 2017
Posts: 860
WE: Supply Chain Management (Energy and Utilities)
Premium Member CAT Tests
Re: A polygon is regular if all the sides are equal and all the interior a  [#permalink]

Show Tags

New post 13 Jul 2018, 09:20
franteraoka wrote:
Thank you so much!PKN


Not mention :-) . You are always welcome franteraoka
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

GMAT Club Bot
Re: A polygon is regular if all the sides are equal and all the interior a &nbs [#permalink] 13 Jul 2018, 09:20
Display posts from previous: Sort by

A polygon is regular if all the sides are equal and all the interior a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.