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

Question

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

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

Alexey1989x · Answer

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

TaN1213 · Answer

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.

stne · Answer

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. Please kindly explain how the answer is C. Thank you. https://gmatclub.com/forum/each-of-the- ... 02190.html

Shbm · Answer

Hey  Bunuel  please provide an explanation for this. I think the answer should be A

ShankSouljaBoi · Answer

Hi ! Can you please explain the OA ?  GMATinsight

GMATinsight · Answer

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) =   = 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

Answer: Option C

GMATinsight · Answer

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) =   = 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

Answer: Option C

I hope this helps!!!

Archit3110 · Answer

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.....

GMATinsight · Answer

Archit3110 The highlighted part "Diametrically opposite points" , by definition, ensures that the line passes through the centre. Refer: https://www.mathwords.com/d/diametrically_opposed.htm

Archit3110 · Answer

GMATinsight : Okay got it sir.. thanks.

houston1980 · Answer

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.

Wadree · Answer

main problem in this question is the use of "a" instead of "the" in the line....."can be diameters of a circle"....using "a" the answer will be 16!......but using "the" answer will be 16.....

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

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