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In the following picture, how many pieces can be pasted when the shape

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Math Revolution GMAT Instructor
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In the following picture, how many pieces can be pasted when the shape  [#permalink]

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New post 13 Nov 2019, 00:49
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Difficulty:

  65% (hard)

Question Stats:

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[GMAT math practice question]

In the following picture, how many pieces can be pasted when the shapes shown on the left are pasted as shown on the right?

Attachment:
11.13ps.png
11.13ps.png [ 20.29 KiB | Viewed 504 times ]


A. \(4\)

B. \(6\)

C. \(8\)

D. \(10 \)

E. \(12\)

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Re: In the following picture, how many pieces can be pasted when the shape  [#permalink]

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New post 13 Nov 2019, 14:43
Basically, we'll get a regular polygon with interior angle = 360-105-105= 150

(n-2)*180 = n* 150

n=12

MathRevolution wrote:
[GMAT math practice question]

In the following picture, how many pieces can be pasted when the shapes shown on the left are pasted as shown on the right?

Attachment:
11.13ps.png


A. \(4\)

B. \(6\)

C. \(8\)

D. \(10 \)

E. \(12\)
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8243
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: In the following picture, how many pieces can be pasted when the shape  [#permalink]

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New post 15 Nov 2019, 01:45
1
=>

When we put two trapezoids together as follows, we have \(∠x = 360° - 2*105° = 75°\) and \(∠BAC = 30°.\)

Attachment:
11.13ps(a).png
11.13ps(a).png [ 14.78 KiB | Viewed 327 times ]


Since \(\frac{360°}{30°} = 12\), we can put in \(12\) triangles or \(12\) trapezoids.

Therefore, E is the answer.
Answer: E
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Re: In the following picture, how many pieces can be pasted when the shape  [#permalink]

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New post 20 Nov 2019, 02:15
As we can see from the sample figure, it forms a regular polygon with an internal angle of 150 degrees.

(n-2)*180 = 150*n.
On solving we get n = 12.

OA - E

MathRevolution wrote:
[GMAT math practice question]

In the following picture, how many pieces can be pasted when the shapes shown on the left are pasted as shown on the right?

Attachment:
11.13ps.png


A. \(4\)

B. \(6\)

C. \(8\)

D. \(10 \)

E. \(12\)
Intern
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Joined: 24 Mar 2018
Posts: 10
Re: In the following picture, how many pieces can be pasted when the shape  [#permalink]

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New post 21 Nov 2019, 06:01
75*2 = 150 = 180*(n-2)/n
Hence, n = 12
GMAT Club Bot
Re: In the following picture, how many pieces can be pasted when the shape   [#permalink] 21 Nov 2019, 06:01
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