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

It is currently 07 Dec 2019, 06:31

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

Which of the following could be the number of diagonals of an n-polygo

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 12 Mar 2019, 00:43
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

49% (01:46) correct 51% (01:12) wrong based on 35 sessions

HideShow timer Statistics

[GMAT math practice question]

Which of the following could be the number of diagonals of an n-polygon?

A. 3
B. 6
C. 8
D. 12
E. 20

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
S
Joined: 19 Jan 2019
Posts: 110
Re: Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 12 Mar 2019, 10:31
sameeruce08 wrote:
Wrong question

Posted from my mobile device


I think the question is asking the maximum number of diagonals a polygon can have.... An octagon has 20 diagonals, that's why the OA is E.... the next polygon is enneagon with 27 diagonals.... But the maximum number given in answer choices is 20... And that's why it's E ..
Intern
Intern
avatar
B
Joined: 11 Apr 2017
Posts: 21
Location: India
Concentration: General Management, Strategy
Schools: ISB '21, IIMA , IIMB, IIMC , XLRI
GPA: 4
WE: General Management (Energy and Utilities)
Re: Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 12 Mar 2019, 11:03
An 8 sided polygon will havde 20 diagonal
diagonal of a polygon=n(n-3)/2
put integers values of n from 4 to 8
only option E is possible
IMO-E
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 12 Mar 2019, 15:53
MathRevolution wrote:
[GMAT math practice question]

Which of the following could be the number of diagonals of an n-polygon?

A. 3
B. 6
C. 8
D. 12
E. 20

\(?\,\,\,:\,\,\,\# \,d\,\,\underline {{\rm{could}}\,\,{\rm{be}}} \,\,\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} \,\,\left( * \right)\,,\,\,N{\rm{ - polygon}}} \right)\)

\(d\,\, \to \,\,\,\left\{ \matrix{
\,{\rm{each}}\,\,{\rm{vertex}}\,\,{\rm{with}}\,\,\left( {{\rm{not}}\,\,{\rm{itself}}} \right)\,\,{\rm{nor}}\,\,\left( {{\rm{next \,\, to}}\,\,{\rm{it}}\,\,{\rm{vertex}}} \right) \hfill \cr
\,\left[ {A - C} \right]\,\,{\rm{diagonal}}\,\,{\rm{is}}\,\,{\rm{the}}\,\,{\rm{same}}\,\,{\rm{of}}\,\,\left[ {C - A} \right]\,\,{\rm{diagonal}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,d = {{N\left( {N - 3} \right)} \over 2}\)

Alternate argument: (Explain!)

\(d = C\left( {N,2} \right) - N = {{N!} \over {2!\left( {N - 2} \right)!}} - N = {{N\left( {N - 1} \right)} \over 2} - {{2N} \over 2} = {{N\left( {N - 3} \right)} \over 2}\)

\(\left. \matrix{
\left( A \right)\,\,\,{{N\left( {N - 3} \right)} \over 2} = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,N\left( {N - 3} \right) = 6\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\rm{impossible}} \hfill \cr
\left( B \right)\,\,\,{{N\left( {N - 3} \right)} \over 2} = 6\,\,\,\,\, \Rightarrow \,\,\,\,\,N\left( {N - 3} \right) = 12\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\rm{impossible}} \hfill \cr
\left( C \right)\,\,\,{{N\left( {N - 3} \right)} \over 2} = 8\,\,\,\,\, \Rightarrow \,\,\,\,\,N\left( {N - 3} \right) = 16\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\rm{impossible}} \hfill \cr
\left( D \right)\,\,\,{{N\left( {N - 3} \right)} \over 2} = 12\,\,\,\,\, \Rightarrow \,\,\,\,\,N\left( {N - 3} \right) = 24\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\rm{impossible}}\,\,\, \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( E \right)\,\,{\rm{by}}\,\,{\rm{exclusion}}\,\,\,\,\left( {**} \right)\)

\(\left( {**} \right)\,\,\,\,\left( E \right)\,\,\,{{N\left( {N - 3} \right)} \over 2} = 20\,\,\,\,\, \Rightarrow \,\,\,\,\,N\left( {N - 3} \right) = 40\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,N = 8\)


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
Senior Manager
Senior Manager
avatar
P
Joined: 27 Dec 2016
Posts: 309
CAT Tests
Re: Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 12 Mar 2019, 18:33
Number of diagonals can be found using n(n-3)/2 formula. Except E, all options fail to satisfy this equation.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 14 Mar 2019, 01:52
=>

The number of diagonals of an n-polygon is nC2 – n = \(\frac{n(n-1)}{2} – n=\frac{n(n-3)}{2}.\)
If \(n = 4\), then the number of diagonals is 4C2 – 4 = 6 – 4 = 2.
If \(n = 5\), then the number of diagonals is 5C2 – 5 = 10 – 5 = 5.
If \(n = 6\), then the number of diagonals is 6C2 – 6 = 15 – 6 = 9.
If \(n = 7\), then the number of diagonals is 7C2 – 7 = 21 – 7 = 14.
If \(n = 8\), then the number of diagonals is 8C2 – 8 = 28 – 8 = 20.

Therefore, E is the answer.
Answer: E
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5436
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Which of the following could be the number of diagonals of an n-polygo  [#permalink]

Show Tags

New post 17 Mar 2019, 23:06
MathRevolution wrote:
[GMAT math practice question]

Which of the following could be the number of diagonals of an n-polygon?

A. 3
B. 6
C. 8
D. 12
E. 20


diagonal of polygon ; n * (n-3)/2
so solve using given options
say
20= n*(n-3)/2
we get = n= 8 ,-5
n = 8 is max possible value of n
IMO E
GMAT Club Bot
Re: Which of the following could be the number of diagonals of an n-polygo   [#permalink] 17 Mar 2019, 23:06
Display posts from previous: Sort by

Which of the following could be the number of diagonals of an n-polygo

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





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