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05 Dec 2018, 02:09
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E
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Difficulty:
65%
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Question Stats:
57% (02:13) correct
43%
(02:22)
wrong
based on 149
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[Math Revolution GMAT math practice question]
A triangle is formed by connecting three randomly chosen vertices of a hexagon. What is the probability that at least one of the sides of the triangle is also a side of the hexagon?
\(A. \frac{4}{5}\)
\(B. \frac{5}{6}\)
\(C. \frac{7}{8}\)
\(D. \frac{8}{9}\)
\(E. \frac{9}{10}\)
A triangle is formed by connecting three randomly chosen vertices of a hexagon. What is the probability that at least one of the sides of the triangle is also a side of the hexagon?
\(A. \frac{4}{5}\)
\(B. \frac{5}{6}\)
\(C. \frac{7}{8}\)
\(D. \frac{8}{9}\)
\(E. \frac{9}{10}\)
05 Dec 2018, 03:42
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MathRevolution
total possible triangles =6C3=20
Total triangles in which no side is side of hexagon=2(please see attached figure)
so no.of triangles in which atleast one side is side of hexagon=20-2=18
Hence,probability=18/20=9/10
hence E.
Attachments
IMG_20181205_161013886.jpg [ 1.78 MiB | Viewed 3378 times ]
07 Dec 2018, 01:00
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=>
Since the hexagon has \(6\) vertices, and we need to choose \(3\) of them to form the vertices of the triangle, the total number of triangles that can be formed is \(6C3 = 20\).
Note that only the following \(2\) triangles do not include an edge of the hexagon:
12.7.png [ 5.52 KiB | Viewed 3256 times ]
Therefore, the number of the triangles satisfying the original condition is \(18 = 20 – 2.\)
Thus, the probability that the triangle will include an edge of the hexagon is \(\frac{18}{20} = \frac{9}{10}.\)
Therefore, the answer is E.
Answer: E
Since the hexagon has \(6\) vertices, and we need to choose \(3\) of them to form the vertices of the triangle, the total number of triangles that can be formed is \(6C3 = 20\).
Note that only the following \(2\) triangles do not include an edge of the hexagon:
Attachment:
12.7.png [ 5.52 KiB | Viewed 3256 times ]
Therefore, the number of the triangles satisfying the original condition is \(18 = 20 – 2.\)
Thus, the probability that the triangle will include an edge of the hexagon is \(\frac{18}{20} = \frac{9}{10}.\)
Therefore, the answer is E.
Answer: E
