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Data Sufficiency - Area of Circles - Trust the GMAT Diagram?

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bigb62387 Newbie | Next Rank: 10 Posts Default Avatar
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Data Sufficiency - Area of Circles - Trust the GMAT Diagram?

Post Wed Apr 10, 2013 5:51 am
Hello - I was curious if someone could help better explain DS # 117 in the 12th Edition of the OG. I understand the logic, but I have read to NEVER trust diagrams provided on the test for Data Sufficiency portion, so whenever I am provided one, I always try to think of a way to disprove it. Can someone help me identify the flaw in my logic below? Thanks!

"117. In the figure above, points A, B, C, D, and E lie on the 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"

My first thought was "they only say point D lies on the small circle, it does not mention where within the larger circle it lies". So I instantly drew the alternative sketch provided below, with the point D WITHIN radius AC. So here goes the math portion:

Statement 1 does not address point D. Since AB = 3 we know the radius of the small circle, r, is 3, so area(small) = 9pi. Since AB + BC = 3 + 2 = 5, we know the radius of the large circle, R, is 5, so area(big) = 25pi. Difference equals 25pi - 9pi = 14pi. SUFFICIENT.

Statement 2 does address point D, so I would think you could come up with different answers, no? First, let's assume the GMAT's provided drawing is accurate. Since CD + DE = 4 + 1 = 5, the radius of the big circle, R, we know area(big) = 25pi. Thus, diameter of the big circle, D, is 10, then the small diameter, d, can be solved using AD + DE = 10, so AD = d = 6, so small radius, AB, r = 3, so we know area(small) = 9pi. Difference equals 25pi - 9pi = 14pi. BUT, what about the alternative, where D is inside radius AC? Then we know that DE - CD = radius of the big circle, R = 4 - 1 = 3. Thus, the diameter of the small circle, AD, d = AC - CD = R - 1 = 3 - 1 = 2. Thus, the radius of the small circle, r = 1. Then the difference equals 9pi - pi = 8pi. If my logic is correct, then 2 different values can solve the equation with statement 2 remaining true, so this statement should be INSUFFICIENT, no?

So the answer should be A? The official answer provided is D, that each is sufficient alone. Any thoughts? Is my logic on the second version flawed? There is nothing in the statement that says where point D has to be, just "on the smaller circle".

Thanks!


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Post Wed Apr 10, 2013 6:37 am
Since the question references the diagram, we must assume that the points are positioned in the order presented on the diagram. However, since this is a DS question, we can't make assumptions about any distances/lengths based on the diagram alone.

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Brent

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bigb62387 Newbie | Next Rank: 10 Posts Default Avatar
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Post Wed Apr 10, 2013 6:29 am
Awesome, thanks for the fast reply, it was very helpful.

So I just watched that video, and there is a slide that says for DS questions "Figure conforms to information in the question. Figure does not necessarily conform to information in the statements"

So, is it because the the question references the circle that I can then always trust the diagram? The question does say "points A, B, C, D, and E lie on the line", but not necessarily "in that order". So, since the question does not say D is between C and E in plain English, but it does show D is between C and E in the diagram, then I can conclude that the diagram is correct, because it is referenced in the question?

Sorry to be so detailed, but I know I've been burned by assuming diagrams were correct in DS questions before.

Thanks again

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Post Wed Apr 10, 2013 6:03 am
Good idea to distrust DS diagrams. However, there are some things that can't be altered in a diagram.
In this question, the test-makers are telling you that point C lies between points B and D. This information is fixed and can't be altered.
In your solution, you rearranged the points such that point C no longer lies between points B and D.

If anyone is interested, we have a free video that covers what can and cannot be assumed with geometric diagrams on the GMAT: http://www.gmatprepnow.com/module/gmat-geometry?id=863

Cheers,
Brent

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