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# Consider three concentric circles A, B and C of radii 3, 5 and 10 unit

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Math Expert
Joined: 02 Sep 2009
Posts: 65061
Consider three concentric circles A, B and C of radii 3, 5 and 10 unit  [#permalink]

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07 Feb 2020, 06:43
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Difficulty:

55% (hard)

Question Stats:

56% (01:47) correct 44% (02:10) wrong based on 63 sessions

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Consider three concentric circles A, B and C of radii 3, 5 and 10 units respectively. The area of the circle C is what percentage greater than the area enclosed between circles A and B?

A. 625%
B. 525%
C. 400%
D. 194%
E. 6.25%

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Joined: 07 May 2019
Posts: 802
Location: India
Re: Consider three concentric circles A, B and C of radii 3, 5 and 10 unit  [#permalink]

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02 Apr 2020, 05:07
1
Bunuel wrote:
Consider three concentric circles A, B and C of radii 3, 5 and 10 units respectively. The area of the circle C is what percentage greater than the area enclosed between circles A and B?

A. 625%
B. 525%
C. 400%
D. 194%
E. 6.25%

Solution:

• Area of triangle A = $$π*3^2 = 9* π$$units
• Area of triangle B =$$π*5^2 = 25* π$$ units
o Area between the triangle A and B = $$25* π – 9* π = 16* π$$ units
• Area of triangle C = $$π*10^2 = 100π$$ units
o Area of triangle C – Area between triangle A and B = $$100* π – 16* π = 84* π$$ units
• The required percentage = $$\frac{84* π}{16* π} *100= 5.25*100 = 525%$$
Hence, the correct answer is Option B.
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Consider three concentric circles A, B and C of radii 3, 5 and 10 unit  [#permalink]

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07 Feb 2020, 06:55
Bunuel wrote:
Consider three concentric circles A, B and C of radii 3, 5 and 10 units respectively. The area of the circle C is what percentage greater than the area enclosed between circles A and B?

A. 625%
B. 525%
C. 400%
D. 194%
E. 6.25%

Area of circle C = $$= 10^2\pi = 100\pi$$
Area enclosed between circle A & B = $$(5^2 - 3^2)\pi = 16 \pi$$
The area of the circle C is what percentage greater than the area enclosed between circles A and B = $$(\frac{100}{16} - 1)*100 \% = \frac{8400}{16} \%= \frac{2100}{4} \%= 525\%$$

IMO B
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Re: Consider three concentric circles A, B and C of radii 3, 5 and 10 unit  [#permalink]

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02 Apr 2020, 10:05
Answer - B) 525%

Approach - Since this is a question of percentage difference, I understood that there would be a ratio which is why I didn't bother even considering the existence of pi and worked simply on the numbers given, which are very workable numbers.

Area enclosed between circles A and B = 25-9 = 16 sq. units.
Area of circle C = 100 sq. units.
Percentage difference = (100-16)/16, = 84/16 which can be simplified to 21/4, which can be calculated to 525%.

Difficulty Level - Very easy, unless there is something that I missed out on reading, given that this has been marked as 700-level question. It took me about 30 seconds to solve this, most of which was spent calculating 21/4.
Re: Consider three concentric circles A, B and C of radii 3, 5 and 10 unit   [#permalink] 02 Apr 2020, 10:05

# Consider three concentric circles A, B and C of radii 3, 5 and 10 unit

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