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03 Apr 2017, 00:35
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
76% (00:47) correct
24%
(00:47)
wrong
based on 94
sessions
History
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The circle above has 5 points on its edge. How many different quadrilaterals can be drawn that use four of these points as its vertices?
A. 120
B. 24
C. 20
D. 5
E. 4
A. 120
B. 24
C. 20
D. 5
E. 4
Good Question +1
Option D
Q. states how many quad.s can be formed using given 5 points on a circle a.k.a. Non-collinear points.
4 points can be chosen out of 5 points in 5C4 ways = 5 ways.
PS - Once 4 points are chosen, one draw multiple shapes using them, i.e., closed structures or just lines passing through all 4 points. But, for every chosen set of 4 points there can be only one UNIQUE quad., as order of points while drawing a quad. doesn't matter.
Hence, in total 5 quad.s can be drawn.
Option D
Q. states how many quad.s can be formed using given 5 points on a circle a.k.a. Non-collinear points.
4 points can be chosen out of 5 points in 5C4 ways = 5 ways.
PS - Once 4 points are chosen, one draw multiple shapes using them, i.e., closed structures or just lines passing through all 4 points. But, for every chosen set of 4 points there can be only one UNIQUE quad., as order of points while drawing a quad. doesn't matter.
Hence, in total 5 quad.s can be drawn.
03 Apr 2017, 07:58
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Bunuel
Slightly different approach:
IMPORTANT: Connecting any 4 points will create a unique quadrilateral.
So, the question really comes down to "In how many different ways can we select 4 of the 5 points?"
From here, one approach is to calculate 5C4 (as RR88 did)
Another approach is to recognize that, if we select 1 point and REMOVE IT, then we are left with 4 points, which can be connected to create a unique quadrilateral.
So, in how many different ways can we select 1 point to REMOVE?
There are 5 points, so there are 5 ways to select 1 point.
Answer:
Cheers,
Brent
