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23 Apr 2018, 21:48
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D
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Question Stats:
82% (00:48) correct
18%
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The total area of the smaller circle is what percent of the total area of the larger circle?
(1) The length of the radius of the larger circle is 300 percent longer than the length of the radius of the smaller circle.
(2) The ratio of the length of the radius of the larger circle to the length of the radius of the smaller circle is 4 to 1.
(1) The length of the radius of the larger circle is 300 percent longer than the length of the radius of the smaller circle.
(2) The ratio of the length of the radius of the larger circle to the length of the radius of the smaller circle is 4 to 1.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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23 Apr 2018, 23:18
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Solution
Given:
• Two circles are there – smaller and larger
To find:
• The total area of the smaller circle is what percent of the total area of the larger circle
Approach and Working:
• If we assume the radius of the smaller circle as r and the radius of the larger circle as R, then
- o Area of the smaller circle = πr2
- o Area of the larger circle = πR2
• Or, if we can find out the ratio of their radii, we can find out the answer
Analysing Statement 1
• As per the information given in Statement 1, R is 300% longer than r.
- o Or, [(R – r)/ r] * 100 = 300
- Solving, R = 4r
- Or, r/R = ¼
- o Therefore, Statement 1 alone is sufficient to answer
Analysing Statement 2
• As per the information given in Statement 2, the ratio of R and r = 4:1
- o Therefore, r/R = 1:4
- o Therefore, Statement 2 alone is sufficient to answer
Answer: D
09 May 2018, 19:57
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Area of smaller circle is what percent of larger circle
RS= radius of smaller
RL= radius of larger
= Area of smaller*100/Area of larger
=πRS^2*100/πRL^2
=((RS/RL)^2)*100
So we simply need ratio of two circles to get answer
I) RL=4RS
RATIO is known can calculate
Sufficient
II)RL=4RS
Ratio is known so sufficient
D is answer
Posted from my mobile device
RS= radius of smaller
RL= radius of larger
= Area of smaller*100/Area of larger
=πRS^2*100/πRL^2
=((RS/RL)^2)*100
So we simply need ratio of two circles to get answer
I) RL=4RS
RATIO is known can calculate
Sufficient
II)RL=4RS
Ratio is known so sufficient
D is answer
Posted from my mobile device
