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pran21
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Do the two circles with centres X and Y touch each other externally? 02 Sep 2014, 01:59
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42% (01:39) correct 58% (01:21) wrong based on 84 sessions

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Do the two circles with centers X and Y touch each other externally?

(1) The distance between X and Y is equal to the diameter of the circle with center X.
(2) One circle is bigger than the other.

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C
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Do the two circles with centres X and Y touch each other externally? 02 Sep 2014, 02:36
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a. NOT SUFFICIENT - The distance between X and Y is equal to the diameter of the circle with center X, in this case there are 3 possibilities
1. When Radius X> Radius Y , diameter of circle with center X is 10(radius 5) and diameter of circle with center Y is 6(radius 3), the circles don't touch in this case, they are 2 units apart (X-Y = 2)
2. Diameter of circle with center X is 6(radius 3) and diameter of circle with center Y is 8(radius 4), the circles intersect internally
3. Circles touch externally, only when radius of X= radius of Y


b. One circle is bigger than the other.
In this case the circles are either apart or intersect internally at two points
Hence, Insufficient

Considering a&b together, rules out the only possibility of equal circles and hence touching externally. This drives us to a single answer 'NO'
Hence a&b together are sufficient
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Do the two circles with centres X and Y touch each other externally? 04 Sep 2014, 09:15
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What if y has a radius of 5 and x has a radius of 2. Couldn't X be located inside Y and not touch externally?
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Do the two circles with centres X and Y touch each other externally? 04 Sep 2014, 09:41
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Hi Saminex,

How can a circle be inside another circle and touch the bigger circle externally ???
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Do the two circles with centres X and Y touch each other externally? 06 Sep 2014, 14:09
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the question is whether or not they touch externally. There is no condition requiring that the circles touch externally. Additionally, overlapping circles do touch externally however if a circle is completely engulfed by another circle then the condition would not be met.

pran21
Hi Saminex,

How can a circle be inside another circle and touch the bigger circle externally ???
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Do the two circles with centres X and Y touch each other externally? 21 Oct 2014, 09:58
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I believe the OA for this question is wrong. Even with the two conditions together, we know nothing about the size of circle with center Y.

Let's say that circle X has radius 5. Then the distance between X and Y is 10. However, Y could have radius 1 (smaller than X) or radius 6 (larger). In the former case, the two don't touch, in the latter, they do.

Even with both statements you have insufficient information.

Answer: E.
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Do the two circles with centres X and Y touch each other externally? 21 Oct 2014, 10:00
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I believe the OA for this question is wrong. Even with the two conditions together, we know nothing about the size of circle with center Y.

Let's say that circle X has radius 5. Then the distance between X and Y is 10. However, Y could have radius 1 (smaller than X) or radius 6 (larger). In the former case, the two don't touch, in the latter, they do.

Even with both statements you have insufficient information.

Answer: E.

Edit: Looking again, it seems the OA is correct. The thing to realize is that "touch externally" means the circles are strictly tangent to one another. I didn't read this as such on the first try. Not sure if GMAT uses this vocabulary or not - anyone have any insight there?
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Do the two circles with centres X and Y touch each other externally? 24 Oct 2014, 00:40
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I had wrong answer but looking at it again I think the OA is correct
Statement 1 => one circle is not inside the other circle
Statement 2=> Thier radius is not the same
Combine, its sufficient, the answer is no.

Bunuel, can you help with this question?
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Do the two circles with centres X and Y touch each other externally? 04 Sep 2016, 04:50
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pran21
Do the two circles with centers X and Y touch each other externally?

(1) The distance between X and Y is equal to the diameter of the circle with center X.
(2) One circle is bigger than the other.
Two circles having centre distance be dia of another will touch externally if both circles are equal.
But statement 2 denies the fact being one greater then other
Thus both circles never touch externally

Ans C

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