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# There are six marked points on the circle above. How many different

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
There are six marked points on the circle above. How many different  [#permalink]

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23 Nov 2017, 22:23
00:00

Difficulty:

25% (medium)

Question Stats:

88% (00:49) correct 12% (01:17) wrong based on 31 sessions

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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 771 times ]

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Math Expert
Joined: 02 Aug 2009
Posts: 7107
Re: There are six marked points on the circle above. How many different  [#permalink]

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25 Nov 2017, 03:56
Bunuel wrote:

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

The Q asks us nothing but to chose 2 out of 6 points so $$6C2 = \frac{6*5}{2}=15$$
D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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There are six marked points on the circle above. How many different  [#permalink]

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25 Nov 2017, 13:46
1
Bunuel wrote:

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:
The attachment 2017-11-23_2025_003.png is no longer available

Attachment:

aaaaaa.png [ 22.6 KiB | Viewed 442 times ]

While I agree that an approach using combinations probably is efficient for most, a very easy pattern exists here.

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)
There are six marked points on the circle above. How many different &nbs [#permalink] 25 Nov 2017, 13:46
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# There are six marked points on the circle above. How many different

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