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

Question

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

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

unraveled · Answer

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

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.

madgmat2019 · Answer

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

Posted from my mobile device

CareerGeek · Answer

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

Archit3110 · Answer

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

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

siddharthkapoor · Answer

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.

ScottTargetTestPrep · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards