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# The LEAST number of trees one would need in order to arrange 4 trees o

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Math Expert
Joined: 02 Sep 2009
Posts: 55148
The LEAST number of trees one would need in order to arrange 4 trees o  [#permalink]

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15 Aug 2017, 02:15
00:00

Difficulty:

15% (low)

Question Stats:

89% (01:07) correct 11% (00:00) wrong based on 29 sessions

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The LEAST number of trees one would need in order to arrange 4 trees on each line of the plan above is

(A) 5
(B) 10
(C) 14
(D) 15
(E) 20

Attachment:

2017-08-15_1311.png [ 3.61 KiB | Viewed 576 times ]

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Re: The LEAST number of trees one would need in order to arrange 4 trees o  [#permalink]

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15 Aug 2017, 02:32

Looking at the figure,
the star is a pentagon and each side of the pentagon is the base of 5 triangles.
So we have a total of 5 trees on each of the vertices of the pentagon.
and one tree each on the 5 triangle's 3rd vertex as two vertices already have a tree.

Hence, we will be have a total of 5+5 = 10 trees(Option B)
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The LEAST number of trees one would need in order to arrange 4 trees o  [#permalink]

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15 Aug 2017, 02:35
Bunuel wrote:

The LEAST number of trees one would need in order to arrange 4 trees on each line of the plan above is

(A) 5
(B) 10
(C) 14
(D) 15
(E) 20

Attachment:
2017-08-15_1311.png

Each lines intersects with other lines at 4 points.
there are a total of 10 intersection points
Hence 10 trees could be placed at these 10 points to satisfy the criteria.
Option B
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Re: The LEAST number of trees one would need in order to arrange 4 trees o  [#permalink]

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15 Aug 2017, 03:05
at all the intersection we can plant a tree ..
so minimum will be 10 .
Re: The LEAST number of trees one would need in order to arrange 4 trees o   [#permalink] 15 Aug 2017, 03:05
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