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20 Oct 2021, 06:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (02:03) correct
38%
(01:49)
wrong
based on 74
sessions
History
Date
Time
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Not Attempted Yet
What is the area of circle ?
(1) The ratio of the circumference of the circle D to the diameter of the circle D is 22/7 :1
(2) The number of the square units of the area of the sector with an angle of measure 60 degree is two times the number of units of the length of an arc with an angle of measure 30 degree.
(1) The ratio of the circumference of the circle D to the diameter of the circle D is 22/7 :1
(2) The number of the square units of the area of the sector with an angle of measure 60 degree is two times the number of units of the length of an arc with an angle of measure 30 degree.
20 Oct 2021, 06:29
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Bunuel
Rephrase the question:
The formula for the area of a circle is \(A = \pi * r^2\). We only need to know \(r\) in order to calculate \(A\). Instead, we could ask: What is the radius of the circle?
Statement 1 Alone:
We can identify \(\frac{22}{7}\) is the approximation of \(\pi\), hence this only tells us \(\frac{C}{d} = \pi\) which is a known formula. Insufficient.
Statement 2 Alone:
Note there is a trap here; if both parts were talking about the same quantity (arc length or sector area), then this would be insufficient as 60 is twice 30, resulting in arc lengths or sector areas having a 2:1 ratio.
In this case, note we have sector area vs arc length, which are supposed to be on two different scales. We were supposed to have \(Area_1 : Area_2 = 2:1\), but instead we have \(Area_1:Length_2 = 2:1\). We can solve for radius now as the left side gives us something in terms of r, hence this is sufficient.
Answer: B
27 Oct 2021, 06:03
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Bunuel
We need the radius to find the area. Lets see if any statements give us that:
(1) The ratio of the circumference of the circle D to the diameter of the circle D is 22/7 :1
\(\frac{2\pi r}{2r} = \frac{22}{7} \)
\(\pi = \frac{22}{7} \)
This is already known , we do not have the value of radius. NOT SUFF.
(2) The number of the square units of the area of the sector with an angle of measure 60 degree is two times the number of units of the length of an arc with an angle of measure 30 degree.
\(\frac{\pi r^2}{6} = 2 *\frac{2 \pi r}{12}\) -> \(\pi r^2 = 2 \pi r\)
\(r^2-2r=0\), \(r(r-2)=0 ,r=0 \) or \(r=2 \)
Since \(r \neq 0 \) , \(r= 2\)
We have the radius . SUFF.
Ans-B
Hope it's clear.
