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11 Sep 2018, 03:09
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
59% (01:07) correct
41%
(00:54)
wrong
based on 46
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the shaded region?
(1) The difference in radius between the inner circle and the outer circle is 5.
(2) Angle x is 45°.
Attachment:
image003.jpg [ 4.71 KiB | Viewed 1915 times ]
11 Sep 2018, 04:23
Kudos
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Bunuel
Question: WHat is the area of shaded region?
Shaded area = \((angle/360)*π(r_1^2 - r_2^2)\)
i.e. We need the angle drawn at the centre by these sectors and \((r_1^2 - r_2^2)\)
Statement 1: The difference in radius between the inner circle and the outer circle is 5
\((r_1^2 - r_2^2) = (r_1-r_2)*(r_1+r_2)\)
We only have the difference of the redie but not the sum and neither do we have the angle x drawn at the centre by the sectors hence
NOT SUFFICIENT
Statement 2: Angle x is 45°
we have the angle x drawn at the centre by the sectors but We do NOT have \((r_1^2 - r_2^2) = (r_1-r_2)*(r_1+r_2)\) hence
NOT SUFFICIENT
After combining the two statements
We only have the difference of the redie and also the angle drawn by sectors at the centre of the circle but we do NOT have the sum of the radie hence
NOT SUFFICIENT
Answer: option E
24 Dec 2022, 03:30
Kudos
Bookmarks
Hi !
This is a classic value based DS question where I have an advantage to NOT solve but simply reason it out without any cumbersome calculation
I need a unique answer for the "area of the shaded region" which is the area between the two circles.
If I knew the area of the larger circle and the smaller circle, I would simply subtract to get to the answer.
Iam sure I dont have that here
and so Iam going to look for the sufficiency of the statement(s) on providing me the radiuses of the two circles. Do I have that?
In any question of circles, I first try to find or establish the centre , move to the radiuses, fill in the data, locate any isosceles or equilateral triangles & finally operate.
I will start with statement 2 since its an easy kill.
It provides Angle x is 45°.
How do I know its the central angle? Where is the radius?
I have no value around area of the circles or anything that leads me to the radius. Insufficient. Eliminate B,D and we are down to 3 options.
In statement 1, we are given "The difference in radius between the inner circle and the outer circle is 5."
Hmm, If the larger circle has radius R and the smaller has r, I am provided with R-r.
I need π(\(R^2\)-\( r^2\)).
Can I compute R+r with only R-r ?? Not without the product Rr. If the product was provided,I could have thought of \((R+r)^2\)-\((R-r)^2\)=4Rr and would have tried to figure out R+r from there.
Can i compute R+r from the figure? Nopes.
Insufficient. Eliminate A. Its either C or E.
Now, what do I have if I combine?
A statement that doesn't provide me R+r and another that gives me some angle within the circle without leading me to R or r in any which ways.
No definite answer when I combine. Eliminate C.
Correct answer E.
Here is an official hard question I explained on circles.
I think this could help the reader apply the visual skills better once they have analysed the question you have posted here.
Devmitra Sen
GMAT Mentor
This is a classic value based DS question where I have an advantage to NOT solve but simply reason it out without any cumbersome calculation
I need a unique answer for the "area of the shaded region" which is the area between the two circles.
If I knew the area of the larger circle and the smaller circle, I would simply subtract to get to the answer.
Iam sure I dont have that here
and so Iam going to look for the sufficiency of the statement(s) on providing me the radiuses of the two circles. Do I have that?In any question of circles, I first try to find or establish the centre , move to the radiuses, fill in the data, locate any isosceles or equilateral triangles & finally operate.
I will start with statement 2 since its an easy kill.
It provides Angle x is 45°.
How do I know its the central angle? Where is the radius?
I have no value around area of the circles or anything that leads me to the radius. Insufficient. Eliminate B,D and we are down to 3 options.
In statement 1, we are given "The difference in radius between the inner circle and the outer circle is 5."
Hmm, If the larger circle has radius R and the smaller has r, I am provided with R-r.
I need π(\(R^2\)-\( r^2\)).
Can I compute R+r with only R-r ?? Not without the product Rr. If the product was provided,I could have thought of \((R+r)^2\)-\((R-r)^2\)=4Rr and would have tried to figure out R+r from there.
Can i compute R+r from the figure? Nopes.
Insufficient. Eliminate A. Its either C or E.
Now, what do I have if I combine?
A statement that doesn't provide me R+r and another that gives me some angle within the circle without leading me to R or r in any which ways.
No definite answer when I combine. Eliminate C.
Correct answer E.
Here is an official hard question I explained on circles.
I think this could help the reader apply the visual skills better once they have analysed the question you have posted here.
Devmitra Sen
GMAT Mentor
