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To create a part for a certain piece of machinery, four equa

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by BTGmoderatorDC » Mon Jan 28, 2019 11:14 pm

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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

OA E

Source: Princeton Review
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by fskilnik@GMATH » Tue Jan 29, 2019 4:16 am
BTGmoderatorDC wrote:Image

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
Source: Princeton Review
$$?\,\,\, = \,\,\,\left[ {\,{{{{360}^ \circ } - \left( {4 \cdot {{18}^ \circ }} \right)} \over {{{360}^ \circ }}}\,} \right] \cdot 100\,\,\left( \% \right)\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{4 \over 5} \cdot 100\left( \% \right)\,\,\, = \,\,\,80\left( \% \right)$$
$$\left( * \right)\,\,{{{{360}^ \circ } - \left( {4 \cdot {{18}^ \circ }} \right)} \over {{{360}^ \circ }}}\,\, = \,\,1 - {{4 \cdot 18} \over {2 \cdot 18 \cdot 10}}\,\, = \,\,1 - {1 \over 5}$$


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

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by Brent@GMATPrepNow » Tue Jan 29, 2019 5:33 am
BTGmoderatorDC wrote:Image

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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by GMATGuruNY » Tue Jan 29, 2019 9:36 am
BTGmoderatorDC wrote:Image

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
The four 18-degree shaded regions = 4*18 = 72 degrees.
The entire circle = 360 degrees.
(shaded regions)/(entire circle) = 72/360 = 1/5.
Thus:
(unshaded regions)/(entire circle) = 1 - 1/5 = 4/5 = 80%.

The correct answer is E.
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by swerve » Tue Jan 29, 2019 11:22 am
Degrees in a circle: 360
4 pieces cut 18 degrees each = 72 degrees cut.

(The area of a circle is proportional to the angle)

% of area remaining: (360-72)/360 = 4/5 ~ 80%.
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