GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Eight points are equally spaced on a circle.
[#permalink]
Updated on: 05 Jun 2019, 08:02
Updated on: 05 Jun 2019, 08:02
2
8
Bookmarks
00:00
Question Stats:
34% (01:50) correct
65% (02:15) wrong based on 73 sessions
Hide Show timer Statistics
Eight points are equally spaced on a circle. If 3 of the 8 points are to be selected at random, what is the probability that a triangle having the 3 points chosen as vertices will be a right triangle?
A) 1/14
B) 1/7
C) 3/14
D) 3/7
E) 6/7
A) 1/14
B) 1/7
C) 3/14
D) 3/7
E) 6/7
Originally posted by AparnaHarri on 31 May 2019, 00:58.
Last edited by Carcass on 05 Jun 2019, 08:02, edited 2 times in total.
Last edited by Carcass on 05 Jun 2019, 08:02, edited 2 times in total.
Edited the OA
Re: Eight points are equally spaced on a circle.
[#permalink]
31 May 2019, 01:48
31 May 2019, 01:48
Expert Reply
Please Sir,
follow the rules for posta on the board https://gre.myprepclub.com/forum/rules-for ... -1083.html.
The title of the question must be appropriate.
Moreover, provide the Official Answer.
Regards
follow the rules for posta on the board https://gre.myprepclub.com/forum/rules-for ... -1083.html.
The title of the question must be appropriate.
Moreover, provide the Official Answer.
Regards
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Eight points are equally spaced on a circle.
[#permalink]
05 Jun 2019, 13:02
05 Jun 2019, 13:02
4
AparnaHarri wrote:
Eight points are equally spaced on a circle. If 3 of the 8 points are to be selected at random, what is the probability that a triangle having the 3 points chosen as vertices will be a right triangle?
A) 1/14
B) 1/7
C) 3/14
D) 3/7
E) 6/7
A) 1/14
B) 1/7
C) 3/14
D) 3/7
E) 6/7
TOUGH question!!!
Key property: An inscribed angle that contains (aka "holds") the DIAMETER will be a 90-degree angle.
For example, let's draw one of the diameters...
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points1.png [ 4.98 KiB | Viewed 16888 times ]
The inscribed angle that contains (aka "holds") the DIAMETER will be a 90-degree angle.
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points2.png [ 6.04 KiB | Viewed 16614 times ]
Likewise, this inscribed angle also contains (aka "holds") the DIAMETER, so it will also be a 90-degree angle.
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points3.png [ 5.78 KiB | Viewed 16625 times ]
So, for the ONE PARTICULAR diameter (shown below)...
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points4.png [ 5.52 KiB | Viewed 16888 times ]
...we can see that, if we make any of the 6 points the 3rd vertex of the triangle, we will get a right triangle.
This means that, FOR EACH diameter in our circle, there are 6 points that will create a right triangle.
Since there are 4 diagonals altogether....
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points5.png [ 6.35 KiB | Viewed 17138 times ]
....we know that the TOTAL number of right triangles possible = (4)(6) = 24
---------------------------------------
Now we need to determine how many different triangles can be created by selecting 3 of the 8 points.
Since the order in which we select the 3 points does not matter, we can use COMBINATIONS.
We can select 3 points from 8 points in 8C3 ways
8C3 = (8)(7)(6)/(3)(2)(1) = 56
-----------------------------------------
So, P(we get a right triangle) = (total number of RIGHT triangles possible)/(total number of triangles possible)
= 24/56
= 3/7
Answer: D
RELATED VIDEO
