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In the circular region with center O, shown above, the two unshaded se

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In the circular region with center O, shown above, the two unshaded se [#permalink]

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New post 23 Nov 2017, 22:28
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In the circular region with center O, shown above, the two unshaded sections comprise 3/7 and 1/3 of the area of the circular region. The shaded section comprises what fractional part of the area of the circular region?

(A) 3/5
(B) 6/7
(C) 2/21
(D) 5/21
(E) 16/21

[Reveal] Spoiler:
Attachment:
2017-11-23_2026.png
2017-11-23_2026.png [ 6.6 KiB | Viewed 346 times ]
[Reveal] Spoiler: OA

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In the circular region with center O, shown above, the two unshaded se [#permalink]

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New post 24 Nov 2017, 05:40
Bunuel wrote:
Image
In the circular region with center O, shown above, the two unshaded sections comprise 3/7 and 1/3 of the area of the circular region. The shaded section comprises what fractional part of the area of the circular region?

(A) 3/5
(B) 6/7
(C) 2/21
(D) 5/21
(E) 16/21

[Reveal] Spoiler:
Attachment:
2017-11-23_2026.png


If the circle will have the entire fraction of the area 1,

the shaded portion will have area \(1 - \frac{3}{7} - \frac{1}{3} = \frac{21 - 9 - 7}{21} = \frac{5}{21}\)

Another method

Assume area of the circle to be 21.

The portion containing \(\frac{3}{7}\) of the circle will have area \(9\)
and the part containing \(\frac{1}{3}\) of the circle to be \(7\).

The shaded portion of the circle will have an area of \(21 - 9 - 7 = 5\)

Hence shaded portion of the circle contains \(\frac{5}{21}\) of the circle(Option D)
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Re: In the circular region with center O, shown above, the two unshaded se [#permalink]

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New post 24 Nov 2017, 05:42
In the circular region with center O, shown above, the two unshaded sections comprise 3/7 and 1/3 of the area of the circular region. The shaded section comprises what fractional part of the area of the circular region?

(A) 3/5
(B) 6/7
(C) 2/21
(D) 5/21
(E) 16/21


Lets x to be the whole area of the circle and y be the shaded section =>

\(x = \frac{3}{7} * x + \frac {1}{3} * x + y\)
\(x = \frac{16x}{21} + y\)
\(y = \frac{21x - 16x}{21}\)
\(y = \frac{5x}{21}\)

The circle area is accaunted to shaded region as 5 : 21
So the answer is D

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Re: In the circular region with center O, shown above, the two unshaded se [#permalink]

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New post 24 Nov 2017, 08:04
First solution is better and lucid...

pushpitkc wrote:
Bunuel wrote:
Image
In the circular region with center O, shown above, the two unshaded sections comprise 3/7 and 1/3 of the area of the circular region. The shaded section comprises what fractional part of the area of the circular region?

(A) 3/5
(B) 6/7
(C) 2/21
(D) 5/21
(E) 16/21

[Reveal] Spoiler:
Attachment:
2017-11-23_2026.png


If the circle will have the entire fraction of the area 1,

the shaded portion will have area \(1 - \frac{3}{7} - \frac{1}{3} = \frac{21 - 9 - 7}{21} = \frac{5}{21}\)

Another method

Assume area of the circle to be 21.

The portion containing \(\frac{3}{7}\) of the circle will have area \(9\)
and the part containing \(\frac{1}{3}\) of the circle to be \(7\).

The shaded portion of the circle will have an area of \(21 - 9 - 7 = 5\)

Hence shaded portion of the circle contains \(\frac{5}{21}\) of the circle(Option D)

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Re: In the circular region with center O, shown above, the two unshaded se   [#permalink] 24 Nov 2017, 08:04
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In the circular region with center O, shown above, the two unshaded se

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