Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 19:44

### 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

# Seventeen different points are to be located on the circumference of a

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56277
Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

14 Nov 2017, 23:45
13
00:00

Difficulty:

95% (hard)

Question Stats:

17% (01:37) correct 83% (01:34) wrong based on 179 sessions

### HideShow timer Statistics

Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34

_________________
Manager
Joined: 05 Dec 2016
Posts: 241
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

15 Nov 2017, 01:09
Each pair forms up only one possible diameter when points are located at strictly opposite sides.
If we are considering "at most" extreme case then all ponts should be evenly distributed on the circumference of the circle, and since we have 17 points, only 16 out of 17 can be placed opposite each other and 17th one would not have a pair.
So there should be 8 possible diameteres at most however if we assume that there could be an overlap, then 17th point can overlap to any other and form up another 9th diameter.
OR maybe some more tricker logic lies behind the correct reasoning of subject problem
Director
Joined: 09 Mar 2017
Posts: 514
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

15 Nov 2017, 09:18
Bunuel wrote:
Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34

imo A - 8
only if two points are exactly opposite to each other,the line joining them would be diameter. 17 points have such 16 points and hence 8 pairs. One point has no point to be connected to as diameter.
_________________
------------------------------
"Trust the timing of your life"
Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq
Director
Joined: 27 May 2012
Posts: 816
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

28 Oct 2018, 13:28
Bunuel wrote:
Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34

Dear Moderator,

Kindly provide the Official explanation for this one, seems as though the Answer should be A.

Here is a similar sum , using the same logic , accordingly the answer here should be A IMO.

https://gmatclub.com/forum/each-of-the- ... 02190.html
_________________
- Stne
Manager
Joined: 20 Jun 2018
Posts: 73
Location: India
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

28 Oct 2018, 20:33
Hey Bunuel please provide an explanation for this. I think the answer should be A
_________________
PLEASE GIVE KUDOS IF YOU WERE ABLE TO SOLVE THE QUESTION. THANK YOU.
Manager
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

03 Nov 2018, 07:03
Hi ! Can you please explain the OA ? GMATinsight
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

Updated on: 03 Nov 2018, 22:55
1
ShankSouljaBoi wrote:
Hi ! Can you please explain the OA ? GMATinsight

Quote:
Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34

ShankSouljaBoi

CONCEPT: A diameter is a line joining two diametrically opposite points on the circumference. i.e. a Diameter requires joining two points

Since we have 17 points so we need to see how many pairs of points can we make

Total pairs of two points = Greatest integer of (17/2) = [17/2] = 8

i.e. There will be 8 distinct diagonals

But since every point is being joined with every other point here therefore total such lines will be 16 as every diagonal will be drawn two
e.g. We will draw a line originating from point 1 to point 9 and then next attempt will be to draw line originating from point 9 and connecting point 1
i.e. Same diameter drawn twice

Hence, total Such lines which become diameter = 8*2 = 16

Attachments

Screenshot 2018-11-04 at 11.07.57 AM.png [ 308.58 KiB | Viewed 769 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 03 Nov 2018, 22:50.
Last edited by GMATinsight on 03 Nov 2018, 22:55, edited 1 time in total.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

03 Nov 2018, 22:54
2
stne wrote:
Bunuel wrote:
Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34

Dear Moderator,

Kindly provide the Official explanation for this one, seems as though the Answer should be A.

Here is a similar sum , using the same logic , accordingly the answer here should be A IMO.

https://gmatclub.com/forum/each-of-the- ... 02190.html

stne and Shbm

Please pay attention to the language of question and then see the explanation here.

The question says, each point is to be connected to all other points by line segments and then At most, how many of the segments thus formed can be diameters of a circle

Check the highlighted, Bold and Italic part which states how many such segments will be diameter that is each segment is to be counted separately irrespective of duplication of the same line therefore,
e.g. We will draw a line originating from point 1 to point 9 and then next attempt will be to draw line originating from point 9 and connecting point 1
i.e. Same diameter drawn twice hence 8 diameters will be counted 16 times

CONCEPT: A diameter is a line joining two diametrically opposite points on the circumference. i.e. a Diameter requires joining two points

Since we have 17 points so we need to see how many pairs of points can we make

Total pairs of two points = Greatest integer of (17/2) = [17/2] = 8

i.e. There will be 8 distinct diagonals

But since every point is being joined with every other point here therefore total such lines will be 16 as every diagonal will be drawn two
e.g. We will draw a line originating from point 1 to point 9 and then next attempt will be to draw line originating from point 9 and connecting point 1
i.e. Same diameter drawn twice

Hence, total Such lines which become diameter = 8*2 = 16

I hope this helps!!!
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4242
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

05 Nov 2018, 06:33
1
GMATinsight: sir, quoting your line below:

concept: "A diameter is a line joining two diametrically opposite points on the circumference. i.e. a Diameter requires joining two points"

For a diameter to be valid on a circle it has to pass through the center as well as 'd=r*2', by your above statement it seems to give definition of a chord of circle... the word 'center' is missing from your statement.

For the question we can also solve it as below:
First drawing a circle and marking 17 points on opposite sides of the circle circumference, we would be left with only 1 point which won't be having any pair, total set of pairs would be 8 or say 16 segments ' diameter' thus be formed on the circle which are all passing through center of the circle,
Had the question not specified the word " diameter ' "how many of the segments thus formed on the circle using 17 points" in that case answer would have been undefined as the position of 17 points wouldn't have be sure.....
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2959
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

06 Nov 2018, 07:36
Archit3110 wrote:
GMATinsight: sir, quoting your line below:

concept: "A diameter is a line joining two diametrically opposite points on the circumference. i.e. a Diameter requires joining two points"

For a diameter to be valid on a circle it has to pass through the center as well as 'd=r*2', by your above statement it seems to give definition of a chord of circle... the word 'center' is missing from your statement.

For the question we can also solve it as below:
First drawing a circle and marking 17 points on opposite sides of the circle circumference, we would be left with only 1 point which won't be having any pair, total set of pairs would be 8 or say 16 segments ' diameter' thus be formed on the circle which are all passing through center of the circle,
Had the question not specified the word " diameter ' "how many of the segments thus formed on the circle using 17 points" in that case answer would have been undefined as the position of 17 points wouldn't have be sure.....

Archit3110

The highlighted part "Diametrically opposite points", by definition, ensures that the line passes through the centre.

Refer: http://www.mathwords.com/d/diametrically_opposed.htm
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4242
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

06 Nov 2018, 11:38
GMATinsight: Okay got it sir.. thanks.
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Manager
Joined: 30 May 2017
Posts: 139
Location: United States
Schools: HBS '21
GMAT 1: 690 Q50 V32
GRE 1: Q168 V164
GPA: 3.57
Re: Seventeen different points are to be located on the circumference of a  [#permalink]

### Show Tags

17 Jan 2019, 04:08
1
Bunuel wrote:
Seventeen different points are to be located on the circumference of a circle and each point is to be connected to all other points by line segments. At most, how many of the segments thus formed can be diameters of a circle?

(A) 8
(B) 9
(C) 16
(D) 17
(E) 34

I personally think the answer to the question is ambiguous. It can be 8 or 16 depending on how you count line segment. I do not see official GMAT asking a question with ambiguous answers.
_________________
Kindly press the +1Kudos if you like the explanation. Thanks a lot!!!
Re: Seventeen different points are to be located on the circumference of a   [#permalink] 17 Jan 2019, 04:08
Display posts from previous: Sort by