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

Question

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

moutikli · Answer

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 If you like my post, please encourage by giving KUDOS :-D

abhijitatprepitt · Answer

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%

JeffTargetTestPrep · Answer

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

fskilnik · Answer

?\,\,\, = \,\,\,\left  \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.

BrentGMATPrepNow · Answer

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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