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To create a part for a certain piece of machinery, four equal-size wed

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To create a part for a certain piece of machinery, four equal-size wed  [#permalink]

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New post Updated on: 10 May 2017, 11:16
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To create a part for a certain piece of machinery, four equal-size wedgeshaped pieces are cut and removed from a circular piece of metal, as illustrated in the diagram above. If the unshaded portion of the circle represents the material remaining after the pieces are removed, what percentage of the original circle remains?

A. 10
B. 20
C. 25
D. 60
E. 80

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Originally posted by SajjadAhmad on 10 May 2017, 11:13.
Last edited by Bunuel on 10 May 2017, 11:16, edited 1 time in total.
Edited the question.
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Re: To create a part for a certain piece of machinery, four equal-size wed  [#permalink]

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New post 10 May 2017, 11:23
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SajjadAhmad wrote:
Attachment:
234.jpg
To create a part for a certain piece of machinery, four equal-size wedgeshaped pieces are cut and removed from a circular piece of metal, as illustrated in the diagram above. If the unshaded portion of the circle represents the material remaining after the pieces are removed, what percentage of the original circle remains?

A. 10
B. 20
C. 25
D. 60
E. 80



IMO, (E) is the answer.

Angle subtended by the unshaded portion = 90 - 18 = 72 degree
Area of the original circle remaining = Area of the 4 unshaded portions = \(\frac{4 * 72 * pi * r ^ 2}{360}\)
So, percentage of the original circle remaining = \(\frac{4 * 72 * pi * r ^ 2 * 100}{pi * r^2 * 360}\)
= 80


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To create a part for a certain piece of machinery, four equal-size wed  [#permalink]

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New post 10 May 2017, 12:13
Degrees in a circle: 360
4 pieces cut 18 deg each = 72 degrees cut.

(Area of a circle is proportional to the angle)

% of area remaining: (360-72)/360 = 4/5 ~ 80%
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Re: To create a part for a certain piece of machinery, four equal-size wed  [#permalink]

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New post 15 May 2017, 16:33
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SajjadAhmad wrote:
Attachment:
234.jpg
To create a part for a certain piece of machinery, four equal-size wedgeshaped pieces are cut and removed from a circular piece of metal, as illustrated in the diagram above. If the unshaded portion of the circle represents the material remaining after the pieces are removed, what percentage of the original circle remains?

A. 10
B. 20
C. 25
D. 60
E. 80


Note that each shaded region corresponds to an 18 degree sector. Since there are four of these sectors, they add up to an 18 x 4 = 72-degree sector. Thus, the remaining material corresponds to a 360 - 72 = 288-degree sector. Since the entire circle has 360 degrees, the remaining material is 288/360 = 8/10 = 80% of the original circle.

Answer: E
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Re: To create a part for a certain piece of machinery, four equal-size wed  [#permalink]

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New post 29 Jan 2019, 05:31
SajjadAhmad wrote:
To create a part for a certain piece of machinery, four equal-size wedgeshaped pieces are cut and removed from a circular piece of metal, as illustrated in the diagram above. If the unshaded portion of the circle represents the material remaining after the pieces are removed, what percentage of the original circle remains?

Image

A. 10
B. 20
C. 25
D. 60
E. 80

\(?\,\,\, = \,\,\,\left[ {\,{{{{360}^ \circ } - \left( {4 \cdot {{18}^ \circ }} \right)} \over {{{360}^ \circ }}}\,} \right] \cdot 100\,\,\left( \% \right)\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{4 \over 5} \cdot 100\left( \% \right)\,\,\, = \,\,\,80\left( \% \right)\)

\(\left( * \right)\,\,{{{{360}^ \circ } - \left( {4 \cdot {{18}^ \circ }} \right)} \over {{{360}^ \circ }}}\,\, = \,\,1 - {{4 \cdot 18} \over {2 \cdot 18 \cdot 10}}\,\, = \,\,1 - {1 \over 5}\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: To create a part for a certain piece of machinery, four equal-size wed  [#permalink]

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New post 29 Jan 2019, 05:45
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Top Contributor
SajjadAhmad wrote:
Attachment:
234.jpg
To create a part for a certain piece of machinery, four equal-size wedgeshaped pieces are cut and removed from a circular piece of metal, as illustrated in the diagram above. If the unshaded portion of the circle represents the material remaining after the pieces are removed, what percentage of the original circle remains?

A. 10
B. 20
C. 25
D. 60
E. 80


IMPORTANT: the diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise.
We can use this fact to solve the question by simply "eyeballing" the diagram.

The question is basically asking us to determine what percent of the circle is NOT shaded.

Well, it's pretty obvious that at least 50% is NOT shaded.
So, we can ELIMINATE A, B and C

We're left with D (60% is NOT shaded) and E (80% is NOT shaded)
I'm pretty confident that the correct answer is MUCH closer to 80% that to 60%, so .....

Answer: E

Cheers,
Brent

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Re: To create a part for a certain piece of machinery, four equal-size wed   [#permalink] 29 Jan 2019, 05:45
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