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23 Nov 2017, 23:23
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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:
88% (00:43) correct
13%
(01:09)
wrong
based on 38
sessions
History
Date
Time
Result
Not Attempted Yet
There are six marked points on the circle above. How many different lines can be drawn that contain two of the marked points?
(A) 5
(B) 6
(C) 12
(D) 15
(E) 30
Attachment:
2017-11-23_2025_003.png [ 4.57 KiB | Viewed 2462 times ]
25 Nov 2017, 04:56
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Bunuel
The Q asks us nothing but to chose 2 out of 6 points so \(6C2 = \frac{6*5}{2}=15\)
D
25 Nov 2017, 14:46
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Bunuel
Attachment:
aaaaaa.png [ 22.6 KiB | Viewed 1974 times ]
The pattern-finding comes in handy when under pressure and, ahem, temporarily grouchy about combinatorics.
The method was not a time-killer. 40 seconds.
Label the points to track on where you started.
Draw, and count, all possible lines from A. There will be
AB, AC, AD, AE, and AF = 5
Draw and count all possible lines from B that do not replicate the line already drawn, AB. There will be
BC, BD, BE, and BF = 4
Draw and count all possible lines from C without replication of lines already drawn. There will be
CD, CE, and CF = 3. Stop.
The pattern is clear: the number of distinct lines that can be drawn from successive points, except F, decreases by 1 for each point.
(You can't draw anything new from F. It has been a point on one of every other letter's lines. Lines drawn from F = 0.)
Number of lines that contain exactly two points = (5 + 4 + 3 + 2 + 1 + 0) = 15
Answer (D)
