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.
Please kindly explain how the answer is C. Thank you.
https://gmatclub.com/forum/each-of-the- ... 02190.html stne and
ShbmPlease 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 circleCheck 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 1i.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 pointsSince 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 diagonalsBut 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 1i.e. Same diameter drawn twice
Hence, total Such lines which become diameter = 8*2 = 16
Answer: Option C
I hope this helps!!!