Q27: In the figure, points A, B, C, D, and E lie on a line. : DS Archive
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# Q27: In the figure, points A, B, C, D, and E lie on a line.

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Manager
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Q27: In the figure, points A, B, C, D, and E lie on a line. [#permalink]

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08 Oct 2006, 23:52
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Q27:

In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?
(1) AB = 3 and BC =2
(2) CD =1 and DE = 4

Am getting D

[color=white]Answer is given as A. What do you guyz think.

My logic for B is also sufficient is

CD + DE = AC = AB + BC

=> AB + BC = 5

AD = AB + BC + CD = 5 + 1 = 6
AB is the radius of the smaller circle and AD is the diameter of the smaller circle. => AB = AD/2 = 3
CE is the radius of the bigger circle = 5

From this we can calculate.
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Director
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09 Oct 2006, 00:05
I got A....

We need to know the area of both of the circles, therefore we need to know the radius of both of the circles...

B) only provides the radius of the larger circle....
Director
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09 Oct 2006, 00:33
Straight A.
using 1, we can get area of both circles (hence desired area), while 2 is insufficent.
Manager
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09 Oct 2006, 06:39
My logic for B is also sufficient is

CD + DE = AC = AB + BC

=> AB + BC = 5

AD = AB + BC + CD = 5 + 1 = 6
AB is the radius of the smaller circle and AD is the diameter of the smaller circle. => AB = AD/2 = 3
CE is the radius of the bigger circle = 5

From this we can calculate.

Manager
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09 Oct 2006, 06:46
I agree with withme.

B gives you enough information to deduce the diameter of the smaller circle, allowing you to find the area. B clearly gives enough information to find the area of the larger circle.

So D it is
SVP
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09 Oct 2006, 06:53
(D) as well.

r = Radius of the small circle
R = Radius of the big circle

Stat1:
o AB = 3 = r
o R = AC = AB + BC = 3 + 2 = 5
SUFF

Stat2:
o R = CE = CD + DE = 1 + 4 = 5
o r = (2*R-DE) /2 = (10-4)/2 = 3
SUFF
Director
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09 Oct 2006, 07:19
In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?
(1) AB = 3 and BC =2
(2) CD =1 and DE = 4

1) 25*pi - 9 *pi Sufficient
2) I can't find the radius of smaller circle so no area

SVP
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09 Oct 2006, 07:34
withme, what is the source of this question?
Director
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09 Oct 2006, 11:28
D

Statement 1:

Radius of smaller circle = AB =3; area = 9pi

Radius of larger circle = AC = 5; area = 25pi SUFF

Statement 2:

Radius of larger circle = CD+DE = 5; area = 25pi

Radius of smaller circle = (DC+CA)/2 = 3; area = 9pi SUFF
Director
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09 Oct 2006, 22:29
withme wrote:
My logic for B is also sufficient is

CD + DE = AC = AB + BC

=> AB + BC = 5

AD = AB + BC + CD = 5 + 1 = 6
AB is the radius of the smaller circle and AD is the diameter of the smaller circle. => AB = AD/2 = 3
CE is the radius of the bigger circle = 5

From this we can calculate.

The problem with your calculation is that from B we do not know what are the values of AB and BC....
Director
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09 Oct 2006, 23:29
cicerone wrote:
SimaQ wrote:
withme wrote:
My logic for B is also sufficient is

CD + DE = AC = AB + BC

=> AB + BC = 5

AD = AB + BC + CD = 5 + 1 = 6
AB is the radius of the smaller circle and AD is the diameter of the smaller circle. => AB = AD/2 = 3
CE is the radius of the bigger circle = 5

From this we can calculate.

Hey simaQ, what's wrong with this logic?
Clearly from 2 statement we get the radius of bigger circle
From the above logic we r getting AB which is the radius of smaller circle.

Ok, yes the answer should be D...
09 Oct 2006, 23:29
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