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13 Sep 2018, 05:05
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (01:40) correct
44%
(02:16)
wrong
based on 68
sessions
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If the area of a sector in a circle is x% of the total area of the circle, what is the measure of the corresponding central angle?
(1) The ratio of the perimeter of the sector to the circumference of the circle is \(\frac{2\pi + 5}{5\pi}\).
(2) x = 40
(1) The ratio of the perimeter of the sector to the circumference of the circle is \(\frac{2\pi + 5}{5\pi}\).
(2) x = 40
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:
Data Sufficiency Forum
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15 Sep 2018, 03:55
Kudos
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If the area of a sector in a circle is x% of the total area of the circle, what is the measure of the corresponding central angle?
(1) The ratio of the perimeter of the sector to the circumference of the circle is \(\frac{2π+5}{5π}\)
perimeter of the sector = \(2r+ rθ = r(2+central angle)\)
circumference central angle of the circle = \(2πr\)
\(\frac{r(2+θ)}{2πr} = \frac{(2π+5)}{5π}\)
\(5(2+θ) = 2(2π+5)\)
\(10+θ=4π+10\)\(θ = 4π\)
sufficient
(2) x = 40
im guessing 25% of the circle means central angle is 90 that is 25% of 360
50% of the circle means central angle is 180 that is 50% of 360
Sector occupies 40% of the total circle so central angle= 40/100*360 = 144
sufficient
Do let me know if the reasoning is right... thanks
(1) The ratio of the perimeter of the sector to the circumference of the circle is \(\frac{2π+5}{5π}\)
perimeter of the sector = \(2r+ rθ = r(2+central angle)\)
circumference central angle of the circle = \(2πr\)
\(\frac{r(2+θ)}{2πr} = \frac{(2π+5)}{5π}\)
\(5(2+θ) = 2(2π+5)\)
\(10+θ=4π+10\)\(θ = 4π\)
sufficient
(2) x = 40
im guessing 25% of the circle means central angle is 90 that is 25% of 360
50% of the circle means central angle is 180 that is 50% of 360
Sector occupies 40% of the total circle so central angle= 40/100*360 = 144
sufficient
Do let me know if the reasoning is right... thanks
28 Feb 2020, 03:02
Kudos
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Bunuel
Solution
Step 1: Analyse Question Stem
- • Let A be the total area of the circle
• Area of sector = x% of A
• Let a be the central angle corresponding to the sector of the circle.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The ratio of the perimeter of the sector to the circumference of the circle is (2π + 5)/5π
Let’s draw the diagram of the circle.
- • Perimeter of the sector = \(\frac{2* π *r*a}{360} + r + r\), where r is the radius of the circle.
• Circumference of the circle = \(2* π *r\)
• \(\frac{(Perimeter\ of\ sector)}{(circumference of the circle)}\)=\(\frac{\frac{2* π *r*a}{360} + 2*r}{2* π *r}= \frac{2*r(π *a+360)}{360*2* π *r} =\frac{( π *r*a + 360)}{360* π}\)
- o \(\frac{(π *a + 360)}{360* π} = \frac{(2π + 5)}{5π}\)
o \(Π*a + 360 = 72(2 π+5)\)
o We can solve this equation to find the value of \(a\).
Statement 2: x =40%
- • We know that for 100% central angle is 360
- o By using the unitary method, we can find the central angle for 40%, which is the value of a.
