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# In the figure, points A, B, C, D, and E lie on a line. A is

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Manager
Joined: 22 Feb 2006
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In the figure, points A, B, C, D, and E lie on a line. A is  [#permalink]

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28 Oct 2009, 14:59
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75% (hard)

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50% (00:39) correct 50% (03:51) wrong based on 237 sessions

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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

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Joined: 29 Aug 2007
Posts: 2359
Re: DS: Area between circles  [#permalink]

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28 Oct 2009, 17:41
TriColor wrote:
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

--------

A.
From 1, we know the radii of the circles. SUFF..
From 2, we know the radius of only the large circle. NSF..

Update: Agree with D. Can get the d or r for small circle from 2.
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Senior Manager
Joined: 18 Aug 2009
Posts: 275
Re: DS: Area between circles  [#permalink]

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28 Oct 2009, 19:28
2
I remember this Q from maybe OG12? and also remember getting this wrong

D

(A) as mentioned, both radius can be calculated. Area 25pi-9pi. Sufficient.
(B) CD=1, DE=4, CE, Big circle radius = 5
AC=5 (CA=CE), CD=1, AD -> Small circle diameter = 6, radius = 3. Area 25pi-9pi. Sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 52388
Re: DS: Area between circles  [#permalink]

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29 Oct 2009, 00:39
I have some doubts about D. I got suspicious because I always beware of tricks when GMAT gives some drawings of figure. How do we know that this figure is drawn to scale?

In the figure we see that the point C (center of the bigger circle) is in the smaller circle, BUT it can be outside of it when the small circle diameter is less than the radius of the bigger.

In that case:

We are still able to answer the question with (1) as it doesn't change a thing for it: sufficient.

But for (2) CD = 1 and DE = 4 --> R=CD+DE=4+1=5, r=(2R-DE)/2=3 --> R=5, r=3.
OR
If C lies outside the smaller circle, CD = 1 and DE = 4. R=DE-CD=4-1=3, r=(R-CD)/2=(3-1)/2=1. R=3, r=1.
As we have different R and r, the area of the region inside the larger circle and outside the smaller circle would be different in each case. Not sufficient.

Probably the most confusing thing here is that when we are dealing with (2) we already know R and r from (1) and it's more difficult to point out the trick, since you get the same R and r for (2) as well and thinking that "OK the same thing sufficient" forgetting to check whether C really lies inside the smaller circle or not.
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Re: DS: Area between circles  [#permalink]

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29 Oct 2009, 00:51
Bunuel:

I am not sure about this...I guess the relative positioning of the points can be trusted even for diagrams. Only the size of line segments and angles can be something which "cant be drawn to scale". For example, if in this diagram we increase or decrease the scale, then also the relative position of points will be the same !
Math Expert
Joined: 02 Sep 2009
Posts: 52388
Re: DS: Area between circles  [#permalink]

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29 Oct 2009, 01:05
Economist wrote:
Bunuel:

I am not sure about this...I guess the relative positioning of the points can be trusted even for diagrams. Only the size of line segments and angles can be something which "cant be drawn to scale". For example, if in this diagram we increase or decrease the scale, then also the relative position of points will be the same !

This would be interesting to find out: what should we "trust" in drawing and what not to. Let's wait for OA and OE. Plus maybe any GMAT tutor wants to bring the light to this problem.
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Manager
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Re: DS: Area between circles  [#permalink]

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29 Oct 2009, 04:02
statement 1:
==========
suff since we know the radius of both the circles.

statement 2:
==========
we can find the radius of larger circle. We can also find the diameter of the smaller circle,we can calculate the radius of the smaller circle.

I will choose option D
Senior Manager
Joined: 18 Aug 2009
Posts: 275
Re: DS: Area between circles  [#permalink]

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29 Oct 2009, 05:31
@ Economist and Bunuel:

I agree with Economist here... Also OA is D. This problem is from OG 12: DS - Q.117
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Re: In the figure, points A, B, C, D, and E lie on a line. A is  [#permalink]

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10 Jul 2018, 20:05
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Re: In the figure, points A, B, C, D, and E lie on a line. A is &nbs [#permalink] 10 Jul 2018, 20:05
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