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Each of the 39 points is placed either inside or on the surface of a

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Bunuel
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Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   21 Oct 2019, 21:28
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Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38
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B
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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   21 Oct 2019, 21:57
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Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38

Points touching surface of the sphere = 60/100 * 39 = 23.4
Now number of diameters formed using these points = 23.4/2 = 11.7

Since maximum points can be only 60%, total maximum diameters possible are = 11.

IMO Answer B.
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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   21 Oct 2019, 22:39
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60%of 39 points is 23....

To draw a diameter we need 2points on the surface of sphere.

So max of 11diametrs can be drawn.


OA:B

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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   21 Oct 2019, 23:25
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Total points = 39
60% of 39 = 60/100*39 = 23.4
Maximum number of points touching the surface = less than 60% = 23 (maximum)

To form a diameter, points have to be arranged exactly opposite to each other on the surface of the sphere
To form 1 diametric chord, we need 2 points
--> From 23 points, we can form a maximum of 22/2 = 11 chords

IMO Option B
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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   22 Oct 2019, 03:03
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39*.6 ~ 23 points
for diameter two points have to be opposite sides ; max possible 11 chords as diameter
IMO B

Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38
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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   22 Oct 2019, 10:53
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Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38


Maximum number of points on the perfect surface=60% of 39=23.4~23 points

The diameter can be drawn only when points on the surface are joined by a line passing through the center of the sphere.

So, in this case, the maximum number of chords that are diameters=23/2=11.5~11.

Therefore, the correct answer is option B.
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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   26 Oct 2019, 08:54
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Bunuel wrote:

Competition Mode Question



Each of the 39 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?

A. 7
B. 11
C. 13
D. 23
E. 38



Since 60% of 39 is 0.6 x 39 = 23.4, we see that fewer than “23.4” points can touch the surface of the sphere. In other words, at most 23 points can be on the surface of the sphere. Assume there are 23 points on the surface of the sphere and all of them are on the equator of the sphere. We can thus have a maximum of 11 distinct pairs of points such that the chord connecting each of these pairs passes through the center of the sphere and thus forms the diameter of the sphere.

Answer: B
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Re: Each of the 39 points is placed either inside or on the surface of a [#permalink] New post   30 Jul 2023, 04:29
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