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Three circles with radii of 1, 2, and 3, lie on the same plane. Do any

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Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed.
(2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Collection of Questions:
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

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New post 30 Jul 2015, 02:07
Bunuel wrote:
Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed.
(2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.



St 1: An equilateral triangle with height 2\(\sqrt{3}\) , then

the side of the triangle a = ( \(\sqrt{3}\) / 2 ) * a = 2 \(\sqrt{3}\)

=> a = 4, which implies that circles with radii 3 and 2 must intersect each other to form a side of eq. triangle = 4.

Hence Sufficient.

St 2: Distance between any two centers < 6

if the distance between any two circles is less than 5, we can confirm that circles with radii 3 and 2 intersect each other.

But since the distance is < 6, then we cannot decide if they intersect each other. Hence not sufficient.

Option A

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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

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New post 30 Jul 2015, 02:24
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Bunuel wrote:
Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed.
(2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.



IMO: A

Statement 1: If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed
Height of an equilateral triangle with side "a' = √3/2*a
2√3 = √3/2 *a
a= 4

If distance between any two centers is 4
For Circles with radius 1 and 2 --> do not intersect
For Circles with radius 1 and 3 --> Touch each other externally
For Circles with radius 2 and 3 --> intersect
Hence suff

Statement 2 : The distance between the centers of any two circles is less than 6.

Maximum distance between any two circles touching externally will be when circle with radius 2 and circle with radius 3 = 5
Thus If distance between them is
below 5 --> intersect
Equal to 5 --> touch externally
>5 --> do not intersect

Given condition distance < 6.
So we get different answers for d=5.5 or 5 or 4
Hence not suff
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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

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Bunuel wrote:
Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed.
(2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.


800score Official Solution:

From Statement (1), we can determine how the circles are positioned relative to each other, because we know the distances between the centers. Therefore, we could establish whether any two of the circles intersect each other or one lies within another. Thus Statement (1) is sufficient. You do NOT need to do any further analysis of Statement (1).

Statement (2) is not sufficient. Imagine the two different situations: all the centers coincide; the centers are the vertices of an equilateral triangle with sides 5.5 . The first situation would answer the original question positively, the second one – negatively. Only if the distance was less than or equaled 5 could we guarantee the positive answer.

Remember that, in Data Sufficiency questions, it is not necessary to solve the problem, it is only necessary to establish whether or not we have sufficient information to do so.

Since Statement (1) is sufficient, and Statement (2) is not, the correct answer is A.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Kudos [?]: 132827 [1], given: 12378

Expert Post
Math Expert
User avatar
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Joined: 02 Sep 2009
Posts: 42269

Kudos [?]: 132827 [0], given: 12378

Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

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New post 17 Aug 2015, 09:21
Bunuel wrote:
Bunuel wrote:
Three circles with radii of 1, 2, and 3, lie on the same plane. Do any of these circles intersect or lie within another?

(1) If you connect the centers of the circles, an equilateral triangle with the height of 2√3 will be formed.
(2) The distance between the centers of any two circles is less than 6.

Kudos for a correct solution.


800score Official Solution:

From Statement (1), we can determine how the circles are positioned relative to each other, because we know the distances between the centers. Therefore, we could establish whether any two of the circles intersect each other or one lies within another. Thus Statement (1) is sufficient. You do NOT need to do any further analysis of Statement (1).

Statement (2) is not sufficient. Imagine the two different situations: all the centers coincide; the centers are the vertices of an equilateral triangle with sides 5.5 . The first situation would answer the original question positively, the second one – negatively. Only if the distance was less than or equaled 5 could we guarantee the positive answer.

Remember that, in Data Sufficiency questions, it is not necessary to solve the problem, it is only necessary to establish whether or not we have sufficient information to do so.

Since Statement (1) is sufficient, and Statement (2) is not, the correct answer is A.


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Hope it helps.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any [#permalink]

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Re: Three circles with radii of 1, 2, and 3, lie on the same plane. Do any   [#permalink] 12 Nov 2017, 20:11
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