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# The centers of the three circles lie on one line (the circles intersec

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Math Expert
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The centers of the three circles lie on one line (the circles intersec  [#permalink]

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01 Feb 2016, 05:09
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Difficulty:

75% (hard)

Question Stats:

43% (01:03) correct 57% (00:56) wrong based on 84 sessions

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The centers of the three circles lie on one line (the circles intersect as shown). What is the area of the shaded part of the figure?

(1) Each of the small circles has a diameter of 5.
(2) The large circle has a radius of 5.

Attachment:

2016-02-01_1608.png [ 4.31 KiB | Viewed 1428 times ]

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Re: The centers of the three circles lie on one line (the circles intersec  [#permalink]

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01 Feb 2016, 05:35
Bunuel wrote:

The centers of the three circles lie on one line (the circles intersect as shown). What is the area of the shaded part of the figure?

(1) Each of the small circles has a diameter of 5.
(2) The large circle has a radius of 5.

Attachment:
2016-02-01_1608.png

Shaded area = Area of Bigger Circle - Area of two smaller circle

i.e. Required Information is "Radius of all three circles or one of the radius and relation of radii of all three circles"

Statement 1: Each of the small circles has a diameter of 5

i.e. both smaller circles have equal radii

i.e. Diameter of Bogger Circle = 2* Diameter of Smaller Circle

and Diameter of Smaller circle = 5, Hence Diameter of Bigger circle = 10. Hence,
SUFFICIENT

Statement 2: The large circle has a radius of 5
We don't know if the two smaller circles have equal or unequal radie hence
NOT SUFFICIENT

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The centers of the three circles lie on one line (the circles intersec  [#permalink]

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01 Feb 2016, 05:44
Bunuel wrote:

The centers of the three circles lie on one line (the circles intersect as shown). What is the area of the shaded part of the figure?

(1) Each of the small circles has a diameter of 5.
(2) The large circle has a radius of 5.

Attachment:
2016-02-01_1608.png

Hi,
A very good Question which tells us What is the limit to the usage of " making use of diagrams drawn to circle scale"?
This Q tells us where we can use it and where we cannot?

the Diagram and the Q tells us that the centers of the three circle is in a line..
1) Using info of the sketch, we can say that the sum of the dia of two smaller one is equal to the dia of larger one
2) What we should not infer is " the two smaller circles are of equal dia" even if you find the two equal through usage of a scale. IF we do that, all Qs relating to Gemetry can be done by just using a scale and an angle measurer.

WHAT IS REQUIRED;-
area of bigger circle and two smaller circles

lets see the statements:-

(1) Each of the small circles has a diameter of 5.
we know the circles are in a line..
and the point 1) of what we can infer can be used to say that the dia of bigger circle is 5+5=10..
Quote:
1) Using info of the sketch, we can say that the sum of the dia of two smaller one is equal to the dia of larger one

we can find area of the three circles, as the radius of all three are known..
Suff

(2) The large circle has a radius of 5.
here use the point 2)..
Quote:
2) What we should not infer is " the two smaller circles are of equal dia" even if you find the two equal through usage of a scale. IF we do that, all Qs relating to Gemetry can be done by just using a scale and an angle measurer.

so smaller circle can have 4 and 6 as diameter or 5 and 5 as diameter..
different areas in different combinations..
Insuff

A
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The centers of the three circles lie on one line (the circles intersec  [#permalink]

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Updated on: 01 Feb 2016, 08:39
chetan2u wrote:
Bunuel wrote:

The centers of the three circles lie on one line (the circles intersect as shown). What is the area of the shaded part of the figure?

(1) Each of the small circles has a diameter of 5.
(2) The large circle has a radius of 5.

Attachment:
2016-02-01_1608.png

Hi,
A very good Question which tells us What is the limit to the usage of " making use of diagrams drawn to circle"?
This Q tells us where we can use it and where we cannot?

chetan2u, you mean "drawn to scale"? If yes, then applying this methodology to DS questions is a straight no. Ballparking can work in PS questions but never in DS as OG does not mention such a thing in the instructions for the DS section.

As for this question, you are not given that the 2 smaller circles are equal in area or have equal radii. Thus without knowing the relative sizes of these smaller circles, you will not be able to answer the question asked.

Per statement 1, dia of each of the 2 smaller circles = 5 units ---> dia of the larger circle = 2*5 = 10 units. Clearly you can now calculate Area of the larger circle - 2* Area of the smaller circles. Sufficient.

Per statement 2, dia of the larger circle does not provide any information on the relative sizes of the 2 smaller circles. Not sufficient. What if the 2 smaller circles have diameters 3 and 7 units respectively or have the diameters 5 units each ? You will end up getting different values for the area of the shaded region.

A is thus the correct answer.

Originally posted by ENGRTOMBA2018 on 01 Feb 2016, 06:25.
Last edited by ENGRTOMBA2018 on 01 Feb 2016, 08:39, edited 1 time in total.
edited the typo
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Re: The centers of the three circles lie on one line (the circles intersec  [#permalink]

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01 Feb 2016, 08:25
1
Engr2012 wrote:
chetan2u wrote:
Bunuel wrote:

Per statement 2, dia of the larger circle does not provide any information on the relative sizes of the 2 smaller circles. Not sufficient. What if the 2 smaller circles have diameters 5 and 7 units respectively or have the diameters 5 units each ? You will end up getting different values for the area of the shaded region.

Just a clarification: I am still trying to understand your explanation.
In statement 2 -- Isn't that, radius of larger circle = diameter of smaller circle? In such case, i think, there is no possibility for 2 diameters (such as 5 & 7 ... 5 & 5).
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Re: The centers of the three circles lie on one line (the circles intersec  [#permalink]

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01 Feb 2016, 08:43
MK1480 wrote:
Engr2012 wrote:

Per statement 2, dia of the larger circle does not provide any information on the relative sizes of the 2 smaller circles. Not sufficient. What if the 2 smaller circles have diameters 5 and 7 units respectively or have the diameters 5 units each ? You will end up getting different values for the area of the shaded region.

Just a clarification: I am still trying to understand your explanation.
In statement 2 -- Isn't that, radius of larger circle = diameter of smaller circle? In such case, i think, there is no possibility for 2 diameters (such as 5 & 7 ... 5 & 5).

I have corrected the typo in my solution. The only condition from the given question is that the diameter of the largest circle = dia1+dia2 (diameters of the 2 smaller circles).

So if you are given that D=10=d1+d2 , then (d1,d2) can either be (3,7) or (5,5). You will end up getting values for the area of the shaded region with these 2 sets of values for the diameters of the smaller circles. Thus statement 2 is NOT sufficient. You are not given that "radius of larger circle = diameter of smaller circle". You are making the mistake of using information from statement 1 to evaluate statement 2. this is not allowed when you are evaluating statements individually.

Hope this helps.
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Re: The centers of the three circles lie on one line (the circles intersec  [#permalink]

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07 Apr 2018, 13:24
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Re: The centers of the three circles lie on one line (the circles intersec   [#permalink] 07 Apr 2018, 13:24
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